Bohr Inequalities on Noncommutative Polydomains View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-02

AUTHORS

Gelu Popescu

ABSTRACT

The goal of this paper is to study the Bohr phenomenon in the setting of free holomorphic functions on noncommutative regular polydomains Dfm, f=(f1,…,fk), generated by positive regular free holomorphic functions. These polydomains are noncommutative analogues of the scalar polydomains Df1(C)×⋯×Dfk(C),where each Dfi(C)⊂Cni is a certain Reinhardt domain generated by fi. We characterize the free holomorphic functions on Dfm in terms of the universal model of the polydomain and extend several classical results from complex analysis to our noncommutative setting. It is shown that the free holomorphic functions admit multi-homogeneous and homogeneous expansions as power series in several variables. With respect to these expansions, we introduce the Bohr radii Kmh(Dfm) and Kh(Dfm) for the noncommutative Hardy space H∞(Df,radm) of all bounded free holomorphic functions on the radial part of Dfm. Several well-known results concerning the Bohr radius associated with classes of bounded holomorphic functions are extended to our noncommutative multivariable setting. More... »

PAGES

7

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00020-019-2505-7

DOI

http://dx.doi.org/10.1007/s00020-019-2505-7

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1111949053


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "The University of Texas at San Antonio", 
          "id": "https://www.grid.ac/institutes/grid.215352.2", 
          "name": [
            "Department of Mathematics, The University of Texas at San Antonio, 78249, San Antonio, TX, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Popescu", 
        "givenName": "Gelu", 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1016/j.aim.2014.07.029", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1003055070"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/s0002-9939-97-04270-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008762718"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/s0002-9947-07-04170-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1015913912"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1515/crll.1916.146.53", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1016142094"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1112/s0024611502013692", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1017385540"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01171120", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1019072371", 
          "https://doi.org/10.1007/bf01171120"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1023/b:simj.0000035827.35563.b6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1024863939", 
          "https://doi.org/10.1023/b:simj.0000035827.35563.b6"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01475487", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025475699", 
          "https://doi.org/10.1007/bf01475487"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01475487", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025475699", 
          "https://doi.org/10.1007/bf01475487"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.aim.2015.02.016", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1028698832"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1112/s0024609306019084", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1037565238"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/s0002-9939-99-05084-4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1039542114"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1112/plms/s2-13.1.1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1039627679"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/mana.3210040124", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1040112791"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jfa.2013.07.015", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044604288"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.aim.2012.07.016", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044613487"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://app.dimensions.ai/details/publication/pub.1046055530", 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-71438-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1046055530", 
          "https://doi.org/10.1007/978-3-642-71438-2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-71438-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1046055530", 
          "https://doi.org/10.1007/978-3-642-71438-2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1006/jfan.1998.3346", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1046120528"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/tran/6466", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1059351363"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2140/apde.2016.9.1185", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069059628"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4007/annals.2011.174.1.13", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1071867343"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.7146/math.scand.a-10653", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1073612784"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.7900/jot.2015dec12.2088", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1074123288"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1515/crelle-2014-0103", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1090514926"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2019-02", 
    "datePublishedReg": "2019-02-01", 
    "description": "The goal of this paper is to study the Bohr phenomenon in the setting of free holomorphic functions on noncommutative regular polydomains Dfm, f=(f1,\u2026,fk), generated by positive regular free holomorphic functions. These polydomains are noncommutative analogues of the scalar polydomains Df1(C)\u00d7\u22ef\u00d7Dfk(C),where each Dfi(C)\u2282Cni is a certain Reinhardt domain generated by fi. We characterize the free holomorphic functions on Dfm in terms of the universal model of the polydomain and extend several classical results from complex analysis to our noncommutative setting. It is shown that the free holomorphic functions admit multi-homogeneous and homogeneous expansions as power series in several variables. With respect to these expansions, we introduce the Bohr radii Kmh(Dfm) and Kh(Dfm) for the noncommutative Hardy space H\u221e(Df,radm) of all bounded free holomorphic functions on the radial part of Dfm. Several well-known results concerning the Bohr radius associated with classes of bounded holomorphic functions are extended to our noncommutative multivariable setting.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s00020-019-2505-7", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isFundedItemOf": [
      {
        "id": "sg:grant.4108359", 
        "type": "MonetaryGrant"
      }
    ], 
    "isPartOf": [
      {
        "id": "sg:journal.1136245", 
        "issn": [
          "0378-620X", 
          "1420-8989"
        ], 
        "name": "Integral Equations and Operator Theory", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "91"
      }
    ], 
    "name": "Bohr Inequalities on Noncommutative Polydomains", 
    "pagination": "7", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "976b9d9f1c0270a8cc220751447d8e22a8595e7f4e26530c144b07e0ea065d9f"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s00020-019-2505-7"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1111949053"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s00020-019-2505-7", 
      "https://app.dimensions.ai/details/publication/pub.1111949053"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T09:09", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000338_0000000338/records_47966_00000002.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://link.springer.com/10.1007%2Fs00020-019-2505-7"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s00020-019-2505-7'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s00020-019-2505-7'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00020-019-2505-7'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00020-019-2505-7'


 

This table displays all metadata directly associated to this object as RDF triples.

137 TRIPLES      21 PREDICATES      51 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s00020-019-2505-7 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N4f4188db195543c5bca9227da1d318a8
4 schema:citation sg:pub.10.1007/978-3-642-71438-2
5 sg:pub.10.1007/bf01171120
6 sg:pub.10.1007/bf01475487
7 sg:pub.10.1023/b:simj.0000035827.35563.b6
8 https://app.dimensions.ai/details/publication/pub.1046055530
9 https://doi.org/10.1002/mana.3210040124
10 https://doi.org/10.1006/jfan.1998.3346
11 https://doi.org/10.1016/j.aim.2012.07.016
12 https://doi.org/10.1016/j.aim.2014.07.029
13 https://doi.org/10.1016/j.aim.2015.02.016
14 https://doi.org/10.1016/j.jfa.2013.07.015
15 https://doi.org/10.1090/s0002-9939-97-04270-6
16 https://doi.org/10.1090/s0002-9939-99-05084-4
17 https://doi.org/10.1090/s0002-9947-07-04170-0
18 https://doi.org/10.1090/tran/6466
19 https://doi.org/10.1112/plms/s2-13.1.1
20 https://doi.org/10.1112/s0024609306019084
21 https://doi.org/10.1112/s0024611502013692
22 https://doi.org/10.1515/crelle-2014-0103
23 https://doi.org/10.1515/crll.1916.146.53
24 https://doi.org/10.2140/apde.2016.9.1185
25 https://doi.org/10.4007/annals.2011.174.1.13
26 https://doi.org/10.7146/math.scand.a-10653
27 https://doi.org/10.7900/jot.2015dec12.2088
28 schema:datePublished 2019-02
29 schema:datePublishedReg 2019-02-01
30 schema:description The goal of this paper is to study the Bohr phenomenon in the setting of free holomorphic functions on noncommutative regular polydomains Dfm, f=(f1,…,fk), generated by positive regular free holomorphic functions. These polydomains are noncommutative analogues of the scalar polydomains Df1(C)×⋯×Dfk(C),where each Dfi(C)⊂Cni is a certain Reinhardt domain generated by fi. We characterize the free holomorphic functions on Dfm in terms of the universal model of the polydomain and extend several classical results from complex analysis to our noncommutative setting. It is shown that the free holomorphic functions admit multi-homogeneous and homogeneous expansions as power series in several variables. With respect to these expansions, we introduce the Bohr radii Kmh(Dfm) and Kh(Dfm) for the noncommutative Hardy space H∞(Df,radm) of all bounded free holomorphic functions on the radial part of Dfm. Several well-known results concerning the Bohr radius associated with classes of bounded holomorphic functions are extended to our noncommutative multivariable setting.
31 schema:genre research_article
32 schema:inLanguage en
33 schema:isAccessibleForFree false
34 schema:isPartOf N03b263316ed143c5a42f3b047eb8673a
35 N9311fb253d714466bf54ee6ec8fae449
36 sg:journal.1136245
37 schema:name Bohr Inequalities on Noncommutative Polydomains
38 schema:pagination 7
39 schema:productId N12e24c31194a49aa9fb1f7c861e942cc
40 N6d68ae0d15bf485b9c010e8811490cfa
41 Nc1a0a3c95ab54c13ba5d8d8f63bb98c1
42 schema:sameAs https://app.dimensions.ai/details/publication/pub.1111949053
43 https://doi.org/10.1007/s00020-019-2505-7
44 schema:sdDatePublished 2019-04-11T09:09
45 schema:sdLicense https://scigraph.springernature.com/explorer/license/
46 schema:sdPublisher Nb3f55a9187ad47f0a95e754876bbb85d
47 schema:url https://link.springer.com/10.1007%2Fs00020-019-2505-7
48 sgo:license sg:explorer/license/
49 sgo:sdDataset articles
50 rdf:type schema:ScholarlyArticle
51 N03b263316ed143c5a42f3b047eb8673a schema:volumeNumber 91
52 rdf:type schema:PublicationVolume
53 N12e24c31194a49aa9fb1f7c861e942cc schema:name readcube_id
54 schema:value 976b9d9f1c0270a8cc220751447d8e22a8595e7f4e26530c144b07e0ea065d9f
55 rdf:type schema:PropertyValue
56 N4f4188db195543c5bca9227da1d318a8 rdf:first Nd7d71f05d95b467ea96fcc87670e58cb
57 rdf:rest rdf:nil
58 N6d68ae0d15bf485b9c010e8811490cfa schema:name doi
59 schema:value 10.1007/s00020-019-2505-7
60 rdf:type schema:PropertyValue
61 N9311fb253d714466bf54ee6ec8fae449 schema:issueNumber 1
62 rdf:type schema:PublicationIssue
63 Nb3f55a9187ad47f0a95e754876bbb85d schema:name Springer Nature - SN SciGraph project
64 rdf:type schema:Organization
65 Nc1a0a3c95ab54c13ba5d8d8f63bb98c1 schema:name dimensions_id
66 schema:value pub.1111949053
67 rdf:type schema:PropertyValue
68 Nd7d71f05d95b467ea96fcc87670e58cb schema:affiliation https://www.grid.ac/institutes/grid.215352.2
69 schema:familyName Popescu
70 schema:givenName Gelu
71 rdf:type schema:Person
72 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
73 schema:name Mathematical Sciences
74 rdf:type schema:DefinedTerm
75 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
76 schema:name Pure Mathematics
77 rdf:type schema:DefinedTerm
78 sg:grant.4108359 http://pending.schema.org/fundedItem sg:pub.10.1007/s00020-019-2505-7
79 rdf:type schema:MonetaryGrant
80 sg:journal.1136245 schema:issn 0378-620X
81 1420-8989
82 schema:name Integral Equations and Operator Theory
83 rdf:type schema:Periodical
84 sg:pub.10.1007/978-3-642-71438-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046055530
85 https://doi.org/10.1007/978-3-642-71438-2
86 rdf:type schema:CreativeWork
87 sg:pub.10.1007/bf01171120 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019072371
88 https://doi.org/10.1007/bf01171120
89 rdf:type schema:CreativeWork
90 sg:pub.10.1007/bf01475487 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025475699
91 https://doi.org/10.1007/bf01475487
92 rdf:type schema:CreativeWork
93 sg:pub.10.1023/b:simj.0000035827.35563.b6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024863939
94 https://doi.org/10.1023/b:simj.0000035827.35563.b6
95 rdf:type schema:CreativeWork
96 https://app.dimensions.ai/details/publication/pub.1046055530 schema:CreativeWork
97 https://doi.org/10.1002/mana.3210040124 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040112791
98 rdf:type schema:CreativeWork
99 https://doi.org/10.1006/jfan.1998.3346 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046120528
100 rdf:type schema:CreativeWork
101 https://doi.org/10.1016/j.aim.2012.07.016 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044613487
102 rdf:type schema:CreativeWork
103 https://doi.org/10.1016/j.aim.2014.07.029 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003055070
104 rdf:type schema:CreativeWork
105 https://doi.org/10.1016/j.aim.2015.02.016 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028698832
106 rdf:type schema:CreativeWork
107 https://doi.org/10.1016/j.jfa.2013.07.015 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044604288
108 rdf:type schema:CreativeWork
109 https://doi.org/10.1090/s0002-9939-97-04270-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008762718
110 rdf:type schema:CreativeWork
111 https://doi.org/10.1090/s0002-9939-99-05084-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039542114
112 rdf:type schema:CreativeWork
113 https://doi.org/10.1090/s0002-9947-07-04170-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015913912
114 rdf:type schema:CreativeWork
115 https://doi.org/10.1090/tran/6466 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059351363
116 rdf:type schema:CreativeWork
117 https://doi.org/10.1112/plms/s2-13.1.1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039627679
118 rdf:type schema:CreativeWork
119 https://doi.org/10.1112/s0024609306019084 schema:sameAs https://app.dimensions.ai/details/publication/pub.1037565238
120 rdf:type schema:CreativeWork
121 https://doi.org/10.1112/s0024611502013692 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017385540
122 rdf:type schema:CreativeWork
123 https://doi.org/10.1515/crelle-2014-0103 schema:sameAs https://app.dimensions.ai/details/publication/pub.1090514926
124 rdf:type schema:CreativeWork
125 https://doi.org/10.1515/crll.1916.146.53 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016142094
126 rdf:type schema:CreativeWork
127 https://doi.org/10.2140/apde.2016.9.1185 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069059628
128 rdf:type schema:CreativeWork
129 https://doi.org/10.4007/annals.2011.174.1.13 schema:sameAs https://app.dimensions.ai/details/publication/pub.1071867343
130 rdf:type schema:CreativeWork
131 https://doi.org/10.7146/math.scand.a-10653 schema:sameAs https://app.dimensions.ai/details/publication/pub.1073612784
132 rdf:type schema:CreativeWork
133 https://doi.org/10.7900/jot.2015dec12.2088 schema:sameAs https://app.dimensions.ai/details/publication/pub.1074123288
134 rdf:type schema:CreativeWork
135 https://www.grid.ac/institutes/grid.215352.2 schema:alternateName The University of Texas at San Antonio
136 schema:name Department of Mathematics, The University of Texas at San Antonio, 78249, San Antonio, TX, USA
137 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...