2013
AUTHORS ABSTRACTA Bochner integral formula \(f = \mathcal{B}-\int_Y w(y)\Phi(y) d\mu(y)\) is derived that presents a function f in terms of weights w and a parametrized family of functions Φ(y), y in Y . Comparison is made to pointwise formulations, norm inequalities relating pointwise and Bochner integrals are established, G-variation and tensor products are studied, and examples are presented. More... »
PAGES183-214
Handbook on Neural Information Processing
ISBN
978-3-642-36656-7
978-3-642-36657-4
http://scigraph.springernature.com/pub.10.1007/978-3-642-36657-4_6
DOIhttp://dx.doi.org/10.1007/978-3-642-36657-4_6
DIMENSIONShttps://app.dimensions.ai/details/publication/pub.1034039933
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/2008/1109",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Neurosciences",
"type": "DefinedTerm"
},
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/11",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Medical and Health Sciences",
"type": "DefinedTerm"
}
],
"author": [
{
"affiliation": {
"alternateName": "Georgetown University",
"id": "https://www.grid.ac/institutes/grid.213910.8",
"name": [
"Department of Mathematics and Statistics, Georgetown University, Washington, D.C., 20057-1233, USA"
],
"type": "Organization"
},
"familyName": "Kainen",
"givenName": "Paul C.",
"id": "sg:person.013607306243.38",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013607306243.38"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "Georgetown University",
"id": "https://www.grid.ac/institutes/grid.213910.8",
"name": [
"Department of Mathematics and Statistics, Georgetown University, Washington, D.C., 20057-1233, USA"
],
"type": "Organization"
},
"familyName": "Vogt",
"givenName": "Andrew",
"id": "sg:person.011266447107.50",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011266447107.50"
],
"type": "Person"
}
],
"citation": [
{
"id": "sg:pub.10.1007/s10957-008-9471-6",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1003582152",
"https://doi.org/10.1007/s10957-008-9471-6"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-642-88044-5",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1004046727",
"https://doi.org/10.1007/978-3-642-88044-5"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-642-88044-5",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1004046727",
"https://doi.org/10.1007/978-3-642-88044-5"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1090/s0002-9947-1950-0051437-7",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1008121516"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-1-4612-1996-5_16",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1008720603",
"https://doi.org/10.1007/978-1-4612-1996-5_16"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-1-4612-1996-5_16",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1008720603",
"https://doi.org/10.1007/978-1-4612-1996-5_16"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/j.jco.2008.08.001",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1012924594"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/s0893-6080(98)00039-2",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1015076901"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-540-70781-3",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1015906782",
"https://doi.org/10.1007/978-3-540-70781-3"
],
"type": "CreativeWork"
},
{
"id": "https://app.dimensions.ai/details/publication/pub.1015906782",
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/s0893-6080(97)00028-2",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1018224020"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/1385-7258(82)90030-0",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1020107506"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1006/jath.1996.0031",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1024100031"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1162/neco.2008.20.1.252",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1033187062"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1162/neco.2009.04-08-745",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1038280951"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/j.jat.2006.12.009",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1043148184"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1002/9781118033241.ch0",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1049750135"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-642-04274-4_73",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1049766865",
"https://doi.org/10.1007/978-3-642-04274-4_73"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s10957-009-9620-6",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1050964880",
"https://doi.org/10.1007/s10957-009-9620-6"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s10957-009-9620-6",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1050964880",
"https://doi.org/10.1007/s10957-009-9620-6"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1063/1.3034115",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1057895569"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1109/18.256500",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1061098999"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1109/18.256500",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1061098999"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1109/18.256500",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1061098999"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1109/18.971754",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1061101835"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1109/tit.2010.2090198",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1061653021"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1119/1.1972842",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1062243952"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1137/070687293",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1062851080"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1147/rd.383.0277",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1063182064"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.2969/jmsj/04020331",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1070931414"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-322-86274-7_1",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1089714464",
"https://doi.org/10.1007/978-3-322-86274-7_1"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.4064/fm-20-1-262-176",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1091682947"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1090/coll/031",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1098741925"
],
"type": "CreativeWork"
}
],
"datePublished": "2013",
"datePublishedReg": "2013-01-01",
"description": "A Bochner integral formula \\(f = \\mathcal{B}-\\int_Y w(y)\\Phi(y) d\\mu(y)\\) is derived that presents a function f in terms of weights w and a parametrized family of functions \u03a6(y), y in Y . Comparison is made to pointwise formulations, norm inequalities relating pointwise and Bochner integrals are established, G-variation and tensor products are studied, and examples are presented.",
"editor": [
{
"familyName": "Bianchini",
"givenName": "Monica",
"type": "Person"
},
{
"familyName": "Maggini",
"givenName": "Marco",
"type": "Person"
},
{
"familyName": "Jain",
"givenName": "Lakhmi C.",
"type": "Person"
}
],
"genre": "chapter",
"id": "sg:pub.10.1007/978-3-642-36657-4_6",
"inLanguage": [
"en"
],
"isAccessibleForFree": false,
"isPartOf": {
"isbn": [
"978-3-642-36656-7",
"978-3-642-36657-4"
],
"name": "Handbook on Neural Information Processing",
"type": "Book"
},
"name": "Bochner Integrals and Neural Networks",
"pagination": "183-214",
"productId": [
{
"name": "doi",
"type": "PropertyValue",
"value": [
"10.1007/978-3-642-36657-4_6"
]
},
{
"name": "readcube_id",
"type": "PropertyValue",
"value": [
"a22861fa9cdfc24a995610410d1d49bd322f6a4d3a63f12cbb54647b6c69145c"
]
},
{
"name": "dimensions_id",
"type": "PropertyValue",
"value": [
"pub.1034039933"
]
}
],
"publisher": {
"location": "Berlin, Heidelberg",
"name": "Springer Berlin Heidelberg",
"type": "Organisation"
},
"sameAs": [
"https://doi.org/10.1007/978-3-642-36657-4_6",
"https://app.dimensions.ai/details/publication/pub.1034039933"
],
"sdDataset": "chapters",
"sdDatePublished": "2019-04-15T21:59",
"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/v90/0000000001_0000000264/records_8693_00000264.jsonl",
"type": "Chapter",
"url": "http://link.springer.com/10.1007/978-3-642-36657-4_6"
}
]Download the RDF metadata as: json-ld nt turtle xml License info
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.10.1007/978-3-642-36657-4_6'
N-Triples is a line-based linked data format ideal for batch operations.
curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-36657-4_6'
Turtle is a human-readable linked data format.
curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-36657-4_6'
RDF/XML is a standard XML format for linked data.
curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-36657-4_6'
This table displays all metadata directly associated to this object as RDF triples.
172 TRIPLES
23 PREDICATES
55 URIs
20 LITERALS
8 BLANK NODES