Norm Resolvent Convergence of Discretized Fourier Multipliers View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2021-08-09

AUTHORS

Horia Cornean, Henrik Garde, Arne Jensen

ABSTRACT

We prove norm estimates for the difference of resolvents of operators and their discrete counterparts, embedded into the continuum using biorthogonal Riesz sequences. The estimates are given in the operator norm for operators on square integrable functions, and depend explicitly on the mesh size for the discrete operators. The operators are a sum of a Fourier multiplier and a multiplicative potential. The Fourier multipliers include the fractional Laplacian and the pseudo-relativistic free Hamiltonian. The potentials are real, bounded, and Hölder continuous. As a side-product, the Hausdorff distance between the spectra of the resolvents of the continuous and discrete operators decays with the same rate in the mesh size as for the norm resolvent estimates. The same result holds for the spectra of the original operators in a local Hausdorff distance. More... »

PAGES

71

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00041-021-09876-5

DOI

http://dx.doi.org/10.1007/s00041-021-09876-5

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1140292458


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/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "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"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Department of Mathematical Sciences, Aalborg University, Skjernvej 4A, 9220, Aalborg \u00d8, Denmark", 
          "id": "http://www.grid.ac/institutes/grid.5117.2", 
          "name": [
            "Department of Mathematical Sciences, Aalborg University, Skjernvej 4A, 9220, Aalborg \u00d8, Denmark"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Cornean", 
        "givenName": "Horia", 
        "id": "sg:person.07770170073.57", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07770170073.57"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Mathematics, Aarhus University, Ny Munkegade 118, 8000, Aarhus C, Denmark", 
          "id": "http://www.grid.ac/institutes/grid.7048.b", 
          "name": [
            "Department of Mathematics, Aarhus University, Ny Munkegade 118, 8000, Aarhus C, Denmark"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Garde", 
        "givenName": "Henrik", 
        "id": "sg:person.016572750311.31", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016572750311.31"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Mathematical Sciences, Aalborg University, Skjernvej 4A, 9220, Aalborg \u00d8, Denmark", 
          "id": "http://www.grid.ac/institutes/grid.5117.2", 
          "name": [
            "Department of Mathematical Sciences, Aalborg University, Skjernvej 4A, 9220, Aalborg \u00d8, Denmark"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Jensen", 
        "givenName": "Arne", 
        "id": "sg:person.015240561701.11", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015240561701.11"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/3-540-51783-9_19", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1042538784", 
          "https://doi.org/10.1007/3-540-51783-9_19"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2021-08-09", 
    "datePublishedReg": "2021-08-09", 
    "description": "We prove norm estimates for the difference of resolvents of operators and their discrete counterparts, embedded into the continuum using biorthogonal Riesz sequences. The estimates are given in the operator norm for operators on square integrable functions, and depend explicitly on the mesh size for the discrete operators. The operators are a sum of a Fourier multiplier and a multiplicative potential. The Fourier multipliers include the fractional Laplacian and the pseudo-relativistic free Hamiltonian. The potentials are real, bounded, and H\u00f6lder continuous. As a side-product, the Hausdorff distance between the spectra of the resolvents of the continuous and discrete operators decays with the same rate in the mesh size as for the norm resolvent estimates. The same result holds for the spectra of the original operators in a local Hausdorff distance.", 
    "genre": "article", 
    "id": "sg:pub.10.1007/s00041-021-09876-5", 
    "inLanguage": "en", 
    "isAccessibleForFree": true, 
    "isPartOf": [
      {
        "id": "sg:journal.1042645", 
        "issn": [
          "1069-5869", 
          "1531-5851"
        ], 
        "name": "Journal of Fourier Analysis and Applications", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "4", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "27"
      }
    ], 
    "keywords": [
      "difference of resolvents", 
      "square integrable functions", 
      "discrete operators", 
      "Fourier multipliers", 
      "original operator", 
      "norm resolvent convergence", 
      "norm estimates", 
      "resolvent", 
      "operators", 
      "discrete counterpart", 
      "Riesz sequences", 
      "operator norm", 
      "integrable functions", 
      "mesh size", 
      "multiplicative potential", 
      "multipliers", 
      "fractional Laplacian", 
      "free Hamiltonian", 
      "H\u00f6lder", 
      "Hausdorff distance", 
      "resolvent estimates", 
      "resolvent convergence", 
      "estimates", 
      "continuum", 
      "norms", 
      "function", 
      "sum", 
      "Laplacian", 
      "Hamiltonian", 
      "distance", 
      "spectra", 
      "same results", 
      "convergence", 
      "counterparts", 
      "sequence", 
      "size", 
      "potential", 
      "same rate", 
      "results", 
      "differences", 
      "rate"
    ], 
    "name": "Norm Resolvent Convergence of Discretized Fourier Multipliers", 
    "pagination": "71", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1140292458"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s00041-021-09876-5"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s00041-021-09876-5", 
      "https://app.dimensions.ai/details/publication/pub.1140292458"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-05-10T10:31", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220509/entities/gbq_results/article/article_879.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/s00041-021-09876-5"
  }
]
 

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/s00041-021-09876-5'

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/s00041-021-09876-5'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00041-021-09876-5'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00041-021-09876-5'


 

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

120 TRIPLES      22 PREDICATES      67 URIs      58 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s00041-021-09876-5 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N7187b8cfc7b346e3afab41b7ba05b030
4 schema:citation sg:pub.10.1007/3-540-51783-9_19
5 schema:datePublished 2021-08-09
6 schema:datePublishedReg 2021-08-09
7 schema:description We prove norm estimates for the difference of resolvents of operators and their discrete counterparts, embedded into the continuum using biorthogonal Riesz sequences. The estimates are given in the operator norm for operators on square integrable functions, and depend explicitly on the mesh size for the discrete operators. The operators are a sum of a Fourier multiplier and a multiplicative potential. The Fourier multipliers include the fractional Laplacian and the pseudo-relativistic free Hamiltonian. The potentials are real, bounded, and Hölder continuous. As a side-product, the Hausdorff distance between the spectra of the resolvents of the continuous and discrete operators decays with the same rate in the mesh size as for the norm resolvent estimates. The same result holds for the spectra of the original operators in a local Hausdorff distance.
8 schema:genre article
9 schema:inLanguage en
10 schema:isAccessibleForFree true
11 schema:isPartOf N87b14cd595fc4e508ca58a746bff9c68
12 Nc04ffa73b0c94f3ea992c2f2a2a21ae3
13 sg:journal.1042645
14 schema:keywords Fourier multipliers
15 Hamiltonian
16 Hausdorff distance
17 Hölder
18 Laplacian
19 Riesz sequences
20 continuum
21 convergence
22 counterparts
23 difference of resolvents
24 differences
25 discrete counterpart
26 discrete operators
27 distance
28 estimates
29 fractional Laplacian
30 free Hamiltonian
31 function
32 integrable functions
33 mesh size
34 multiplicative potential
35 multipliers
36 norm estimates
37 norm resolvent convergence
38 norms
39 operator norm
40 operators
41 original operator
42 potential
43 rate
44 resolvent
45 resolvent convergence
46 resolvent estimates
47 results
48 same rate
49 same results
50 sequence
51 size
52 spectra
53 square integrable functions
54 sum
55 schema:name Norm Resolvent Convergence of Discretized Fourier Multipliers
56 schema:pagination 71
57 schema:productId N84f2684d053c49e3ba3d9111dedb0f17
58 Nb634565f007d4ee2b905b0b20de679a9
59 schema:sameAs https://app.dimensions.ai/details/publication/pub.1140292458
60 https://doi.org/10.1007/s00041-021-09876-5
61 schema:sdDatePublished 2022-05-10T10:31
62 schema:sdLicense https://scigraph.springernature.com/explorer/license/
63 schema:sdPublisher N80176ddf888847ada66b733a769f230c
64 schema:url https://doi.org/10.1007/s00041-021-09876-5
65 sgo:license sg:explorer/license/
66 sgo:sdDataset articles
67 rdf:type schema:ScholarlyArticle
68 N2200541596a34b40b8088492108a163b rdf:first sg:person.015240561701.11
69 rdf:rest rdf:nil
70 N7187b8cfc7b346e3afab41b7ba05b030 rdf:first sg:person.07770170073.57
71 rdf:rest N9f4b9e8cb2014d6d948eeafa2860b399
72 N80176ddf888847ada66b733a769f230c schema:name Springer Nature - SN SciGraph project
73 rdf:type schema:Organization
74 N84f2684d053c49e3ba3d9111dedb0f17 schema:name doi
75 schema:value 10.1007/s00041-021-09876-5
76 rdf:type schema:PropertyValue
77 N87b14cd595fc4e508ca58a746bff9c68 schema:volumeNumber 27
78 rdf:type schema:PublicationVolume
79 N9f4b9e8cb2014d6d948eeafa2860b399 rdf:first sg:person.016572750311.31
80 rdf:rest N2200541596a34b40b8088492108a163b
81 Nb634565f007d4ee2b905b0b20de679a9 schema:name dimensions_id
82 schema:value pub.1140292458
83 rdf:type schema:PropertyValue
84 Nc04ffa73b0c94f3ea992c2f2a2a21ae3 schema:issueNumber 4
85 rdf:type schema:PublicationIssue
86 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
87 schema:name Mathematical Sciences
88 rdf:type schema:DefinedTerm
89 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
90 schema:name Pure Mathematics
91 rdf:type schema:DefinedTerm
92 sg:journal.1042645 schema:issn 1069-5869
93 1531-5851
94 schema:name Journal of Fourier Analysis and Applications
95 schema:publisher Springer Nature
96 rdf:type schema:Periodical
97 sg:person.015240561701.11 schema:affiliation grid-institutes:grid.5117.2
98 schema:familyName Jensen
99 schema:givenName Arne
100 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015240561701.11
101 rdf:type schema:Person
102 sg:person.016572750311.31 schema:affiliation grid-institutes:grid.7048.b
103 schema:familyName Garde
104 schema:givenName Henrik
105 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016572750311.31
106 rdf:type schema:Person
107 sg:person.07770170073.57 schema:affiliation grid-institutes:grid.5117.2
108 schema:familyName Cornean
109 schema:givenName Horia
110 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07770170073.57
111 rdf:type schema:Person
112 sg:pub.10.1007/3-540-51783-9_19 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042538784
113 https://doi.org/10.1007/3-540-51783-9_19
114 rdf:type schema:CreativeWork
115 grid-institutes:grid.5117.2 schema:alternateName Department of Mathematical Sciences, Aalborg University, Skjernvej 4A, 9220, Aalborg Ø, Denmark
116 schema:name Department of Mathematical Sciences, Aalborg University, Skjernvej 4A, 9220, Aalborg Ø, Denmark
117 rdf:type schema:Organization
118 grid-institutes:grid.7048.b schema:alternateName Department of Mathematics, Aarhus University, Ny Munkegade 118, 8000, Aarhus C, Denmark
119 schema:name Department of Mathematics, Aarhus University, Ny Munkegade 118, 8000, Aarhus C, Denmark
120 rdf:type schema:Organization
 




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


...