Mapping Properties of the Wave Operators in Scattering Theory View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1992

AUTHORS

A. Jensen

ABSTRACT

We consider the (modified) wave operators for two-body Schrödinger operators with smooth long range potentials. The wave operators and the adjoint wave operators, both localized in energy, are shown to map a weighted L2-space into a slightly larger weighted L2-space. The scattering operator, localized in energy, is shown to be bounded on all the weighted L2-spaces. More... »

PAGES

103-110

Book

TITLE

Approximation by Solutions of Partial Differential Equations

ISBN

978-94-010-5074-6
978-94-011-2436-2

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-94-011-2436-2_11

DOI

http://dx.doi.org/10.1007/978-94-011-2436-2_11

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1051231444


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 Mathematics and Computer Science, Institute for Electronic Systems, Aalborg University, Fredrik Bajers Vej 7, DK-9220, Aalborg \u00d8, Denmark", 
          "id": "http://www.grid.ac/institutes/grid.5117.2", 
          "name": [
            "Department of Mathematics and Computer Science, Institute for Electronic Systems, Aalborg University, Fredrik Bajers Vej 7, DK-9220, Aalborg \u00d8, Denmark"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Jensen", 
        "givenName": "A.", 
        "id": "sg:person.015240561701.11", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015240561701.11"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "1992", 
    "datePublishedReg": "1992-01-01", 
    "description": "We consider the (modified) wave operators for two-body Schr\u00f6dinger operators with smooth long range potentials. The wave operators and the adjoint wave operators, both localized in energy, are shown to map a weighted L2-space into a slightly larger weighted L2-space. The scattering operator, localized in energy, is shown to be bounded on all the weighted L2-spaces.", 
    "editor": [
      {
        "familyName": "Fuglede", 
        "givenName": "B.", 
        "type": "Person"
      }, 
      {
        "familyName": "Goldstein", 
        "givenName": "M.", 
        "type": "Person"
      }, 
      {
        "familyName": "Haussmann", 
        "givenName": "W.", 
        "type": "Person"
      }, 
      {
        "familyName": "Hayman", 
        "givenName": "W. K.", 
        "type": "Person"
      }, 
      {
        "familyName": "Rogge", 
        "givenName": "L.", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-94-011-2436-2_11", 
    "inLanguage": "en", 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "978-94-010-5074-6", 
        "978-94-011-2436-2"
      ], 
      "name": "Approximation by Solutions of Partial Differential Equations", 
      "type": "Book"
    }, 
    "keywords": [
      "energy", 
      "scattering theory", 
      "wave operator", 
      "range potential", 
      "properties", 
      "long range potential", 
      "operators", 
      "potential", 
      "theory", 
      "Schr\u00f6dinger operators", 
      "mapping properties", 
      "L2-space", 
      "weighted L2-spaces", 
      "two-body Schr\u00f6dinger operators", 
      "smooth long range potentials", 
      "adjoint wave operators"
    ], 
    "name": "Mapping Properties of the Wave Operators in Scattering Theory", 
    "pagination": "103-110", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1051231444"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-94-011-2436-2_11"
        ]
      }
    ], 
    "publisher": {
      "name": "Springer Nature", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-94-011-2436-2_11", 
      "https://app.dimensions.ai/details/publication/pub.1051231444"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2022-01-01T19:08", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220101/entities/gbq_results/chapter/chapter_148.jsonl", 
    "type": "Chapter", 
    "url": "https://doi.org/10.1007/978-94-011-2436-2_11"
  }
]
 

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.10.1007/978-94-011-2436-2_11'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-94-011-2436-2_11'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-94-011-2436-2_11'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-94-011-2436-2_11'


 

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

96 TRIPLES      23 PREDICATES      42 URIs      35 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-94-011-2436-2_11 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author Ncb0f56ac8d9b4ce48b2fe47360db1642
4 schema:datePublished 1992
5 schema:datePublishedReg 1992-01-01
6 schema:description We consider the (modified) wave operators for two-body Schrödinger operators with smooth long range potentials. The wave operators and the adjoint wave operators, both localized in energy, are shown to map a weighted L2-space into a slightly larger weighted L2-space. The scattering operator, localized in energy, is shown to be bounded on all the weighted L2-spaces.
7 schema:editor N1116a4f27655462dbc3bdf8b3f09f0cd
8 schema:genre chapter
9 schema:inLanguage en
10 schema:isAccessibleForFree false
11 schema:isPartOf N3b60ce9b7b544af6973417f65e3c6a40
12 schema:keywords L2-space
13 Schrödinger operators
14 adjoint wave operators
15 energy
16 long range potential
17 mapping properties
18 operators
19 potential
20 properties
21 range potential
22 scattering theory
23 smooth long range potentials
24 theory
25 two-body Schrödinger operators
26 wave operator
27 weighted L2-spaces
28 schema:name Mapping Properties of the Wave Operators in Scattering Theory
29 schema:pagination 103-110
30 schema:productId N095c179658a442009b8abb1ef8dce82c
31 N0a932343d1b24a46847ab3299e760fc6
32 schema:publisher N02bea56c5f804f129574e0e7542fc57b
33 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051231444
34 https://doi.org/10.1007/978-94-011-2436-2_11
35 schema:sdDatePublished 2022-01-01T19:08
36 schema:sdLicense https://scigraph.springernature.com/explorer/license/
37 schema:sdPublisher N06cac6dd63a2476c985edc47e9dbbb33
38 schema:url https://doi.org/10.1007/978-94-011-2436-2_11
39 sgo:license sg:explorer/license/
40 sgo:sdDataset chapters
41 rdf:type schema:Chapter
42 N02bea56c5f804f129574e0e7542fc57b schema:name Springer Nature
43 rdf:type schema:Organisation
44 N06cac6dd63a2476c985edc47e9dbbb33 schema:name Springer Nature - SN SciGraph project
45 rdf:type schema:Organization
46 N095c179658a442009b8abb1ef8dce82c schema:name dimensions_id
47 schema:value pub.1051231444
48 rdf:type schema:PropertyValue
49 N0a932343d1b24a46847ab3299e760fc6 schema:name doi
50 schema:value 10.1007/978-94-011-2436-2_11
51 rdf:type schema:PropertyValue
52 N1116a4f27655462dbc3bdf8b3f09f0cd rdf:first N7fca35442a7b49c8a7b526e981d04407
53 rdf:rest N9834912f0a5845d39cf7341c41227d6b
54 N245397e34f7a42bab9cade3a9301cc8f schema:familyName Goldstein
55 schema:givenName M.
56 rdf:type schema:Person
57 N3b60ce9b7b544af6973417f65e3c6a40 schema:isbn 978-94-010-5074-6
58 978-94-011-2436-2
59 schema:name Approximation by Solutions of Partial Differential Equations
60 rdf:type schema:Book
61 N7c9207a1df4548edab2cbd95a93ff3c5 schema:familyName Hayman
62 schema:givenName W. K.
63 rdf:type schema:Person
64 N7fca35442a7b49c8a7b526e981d04407 schema:familyName Fuglede
65 schema:givenName B.
66 rdf:type schema:Person
67 N85da3a97331f4c08b663f7a8ee11431b schema:familyName Rogge
68 schema:givenName L.
69 rdf:type schema:Person
70 N94d85bbf409a4f6ca6a295ac7308bd60 schema:familyName Haussmann
71 schema:givenName W.
72 rdf:type schema:Person
73 N9834912f0a5845d39cf7341c41227d6b rdf:first N245397e34f7a42bab9cade3a9301cc8f
74 rdf:rest Nb7140231614a4dd291281d8681a6930d
75 Nb7140231614a4dd291281d8681a6930d rdf:first N94d85bbf409a4f6ca6a295ac7308bd60
76 rdf:rest Ncf696e8e1f80448daa032fb78a241047
77 Nba811a3e880342c69faa7b8123a2be19 rdf:first N85da3a97331f4c08b663f7a8ee11431b
78 rdf:rest rdf:nil
79 Ncb0f56ac8d9b4ce48b2fe47360db1642 rdf:first sg:person.015240561701.11
80 rdf:rest rdf:nil
81 Ncf696e8e1f80448daa032fb78a241047 rdf:first N7c9207a1df4548edab2cbd95a93ff3c5
82 rdf:rest Nba811a3e880342c69faa7b8123a2be19
83 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
84 schema:name Mathematical Sciences
85 rdf:type schema:DefinedTerm
86 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
87 schema:name Pure Mathematics
88 rdf:type schema:DefinedTerm
89 sg:person.015240561701.11 schema:affiliation grid-institutes:grid.5117.2
90 schema:familyName Jensen
91 schema:givenName A.
92 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015240561701.11
93 rdf:type schema:Person
94 grid-institutes:grid.5117.2 schema:alternateName Department of Mathematics and Computer Science, Institute for Electronic Systems, Aalborg University, Fredrik Bajers Vej 7, DK-9220, Aalborg Ø, Denmark
95 schema:name Department of Mathematics and Computer Science, Institute for Electronic Systems, Aalborg University, Fredrik Bajers Vej 7, DK-9220, Aalborg Ø, Denmark
96 rdf:type schema:Organization
 




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


...