Ontology type: schema:Chapter
1988
AUTHORSAad Dijksma , Heinz Langer , Henk de Snoo
ABSTRACTIn earlier papers [DLS1–6] we have described the selfadjoint extensions, in indefinite inner product spaces and with nonempty resolvent sets of a symmetric closed relation S in a Hilbert space ℌ by means of generalized resolvents, characteristic functions and Štraus extensions. In this paper we show how these results can be applied when S comes from a 2n×2n Hamiltonian system of ordinary differential equations on an interval [a, b), (1.1) Jy′(t) = (ℓΔ(t) + H(t)) y(t) + Δ(t)f(t), t ∈[a, b), ℓ∈ℂ, which is regular in a and in the limit point case in b; for further specifications see Section 5. We pay special attention to selfadjoint extensions beyond the given space ℌ, as they give rise to eigenvalue and boundary value problems with boundary conditions of the form (1.2) A(ℓ)y1 (a) + B(ℓ)y 2 (a) = 0, in which the matrix coefficients A(ℓ) and В(ℓ) depend holomorphically on the eigenvalue parameter ℓ, see Theorem 7.1 below. The eigenvalue problem for such a selfadjoint extension in a larger space can be considered as a linearization of the corresponding boundary value problem (1.1) and (1.2). More... »
PAGES37-83
Contributions to Operator Theory and its Applications
ISBN
978-3-0348-9978-9
978-3-0348-9284-1
http://scigraph.springernature.com/pub.10.1007/978-3-0348-9284-1_3
DOIhttp://dx.doi.org/10.1007/978-3-0348-9284-1_3
DIMENSIONShttps://app.dimensions.ai/details/publication/pub.1045182218
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": "University of Groningen",
"id": "https://www.grid.ac/institutes/grid.4830.f",
"name": [
"Wiskunde En Informatica, Rijksuniversiteit Groningen, Postbus 800, 9700 AV, Groningen, Nederland"
],
"type": "Organization"
},
"familyName": "Dijksma",
"givenName": "Aad",
"id": "sg:person.013762723211.39",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013762723211.39"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "TU Dresden",
"id": "https://www.grid.ac/institutes/grid.4488.0",
"name": [
"Sektion Mathematik, Technische Universit\u00e4t, Mommsenstrasse 13, DDR-8027, Dresden, Germany"
],
"type": "Organization"
},
"familyName": "Langer",
"givenName": "Heinz",
"id": "sg:person.07450173411.71",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07450173411.71"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "University of Groningen",
"id": "https://www.grid.ac/institutes/grid.4830.f",
"name": [
"Wiskunde En Informatica, Rijksuniversiteit Groningen, Postbus 800, 9700 AV, Groningen, Nederland"
],
"type": "Organization"
},
"familyName": "de Snoo",
"givenName": "Henk",
"id": "sg:person.012621265101.72",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012621265101.72"
],
"type": "Person"
}
],
"citation": [
{
"id": "https://doi.org/10.1002/mana.19851200123",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1001182196"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01195919",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1005975786",
"https://doi.org/10.1007/bf01195919"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01195919",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1005975786",
"https://doi.org/10.1007/bf01195919"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-0348-7698-8_15",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1008400943",
"https://doi.org/10.1007/978-3-0348-7698-8_15"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01361930",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1009713231",
"https://doi.org/10.1007/bf01361930"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01361930",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1009713231",
"https://doi.org/10.1007/bf01361930"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-642-65567-8",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1011407145",
"https://doi.org/10.1007/978-3-642-65567-8"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-642-65567-8",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1011407145",
"https://doi.org/10.1007/978-3-642-65567-8"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01076418",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1012320986",
"https://doi.org/10.1007/bf01076418"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01076418",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1012320986",
"https://doi.org/10.1007/bf01076418"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1090/s0002-9947-1960-0133455-x",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1014508014"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01238863",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1017336779",
"https://doi.org/10.1007/bf01238863"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01076361",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1017544425",
"https://doi.org/10.1007/bf01076361"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01076361",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1017544425",
"https://doi.org/10.1007/bf01076361"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/0022-0396(81)90002-4",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1021897629"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01350731",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1030748263",
"https://doi.org/10.1007/bf01350731"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01350731",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1030748263",
"https://doi.org/10.1007/bf01350731"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1090/s0002-9947-1961-0133457-4",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1034314438"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/0022-0396(83)90071-2",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1036040709"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-0348-5483-2_5",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1036362980",
"https://doi.org/10.1007/978-3-0348-5483-2_5"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01202812",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1036849900",
"https://doi.org/10.1007/bf01202812"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01202812",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1036849900",
"https://doi.org/10.1007/bf01202812"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bfb0072441",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1041863154",
"https://doi.org/10.1007/bfb0072441"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/0022-0396(72)90074-5",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1042474221"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01343801",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1045193281",
"https://doi.org/10.1007/bf01343801"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01168461",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1052346154",
"https://doi.org/10.1007/bf01168461"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01168461",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1052346154",
"https://doi.org/10.1007/bf01168461"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1017/s0308210500011951",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1054892928"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1017/s0308210500012312",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1054892964"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1017/s0308210500015365",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1054893241"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1017/s0308210500016516",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1054893356"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1017/s0308210500026196",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1054894302"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1017/s0308210500031942",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1054894876"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1216/rmj-1972-2-1-75",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1064427416"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.2140/pjm.1977.72.135",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1069067067"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.2140/pjm.1986.125.347",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1069069157"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.2307/1993448",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1069688878"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.2307/1993919",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1069688984"
],
"type": "CreativeWork"
}
],
"datePublished": "1988",
"datePublishedReg": "1988-01-01",
"description": "In earlier papers [DLS1\u20136] we have described the selfadjoint extensions, in indefinite inner product spaces and with nonempty resolvent sets of a symmetric closed relation S in a Hilbert space \u210c by means of generalized resolvents, characteristic functions and \u0160traus extensions. In this paper we show how these results can be applied when S comes from a 2n\u00d72n Hamiltonian system of ordinary differential equations on an interval [a, b), (1.1) Jy\u2032(t) = (\u2113\u0394(t) + H(t)) y(t) + \u0394(t)f(t), t \u2208[a, b), \u2113\u2208\u2102, which is regular in a and in the limit point case in b; for further specifications see Section 5. We pay special attention to selfadjoint extensions beyond the given space \u210c, as they give rise to eigenvalue and boundary value problems with boundary conditions of the form (1.2) A(\u2113)y1 (a) + B(\u2113)y 2 (a) = 0, in which the matrix coefficients A(\u2113) and \u0412(\u2113) depend holomorphically on the eigenvalue parameter \u2113, see Theorem 7.1 below. The eigenvalue problem for such a selfadjoint extension in a larger space can be considered as a linearization of the corresponding boundary value problem (1.1) and (1.2).",
"editor": [
{
"familyName": "Gohberg",
"givenName": "I.",
"type": "Person"
},
{
"familyName": "Helton",
"givenName": "J. W.",
"type": "Person"
},
{
"familyName": "Rodman",
"givenName": "L.",
"type": "Person"
}
],
"genre": "chapter",
"id": "sg:pub.10.1007/978-3-0348-9284-1_3",
"inLanguage": [
"en"
],
"isAccessibleForFree": false,
"isPartOf": {
"isbn": [
"978-3-0348-9978-9",
"978-3-0348-9284-1"
],
"name": "Contributions to Operator Theory and its Applications",
"type": "Book"
},
"name": "Hamiltonian Systems with Eigenvalue Depending Boundary Conditions",
"pagination": "37-83",
"productId": [
{
"name": "dimensions_id",
"type": "PropertyValue",
"value": [
"pub.1045182218"
]
},
{
"name": "doi",
"type": "PropertyValue",
"value": [
"10.1007/978-3-0348-9284-1_3"
]
},
{
"name": "readcube_id",
"type": "PropertyValue",
"value": [
"d737f852496a140ca4302f6efc2fa060db0bfc578ab5e659d5c284da4d49e34f"
]
}
],
"publisher": {
"location": "Basel",
"name": "Birkh\u00e4user Basel",
"type": "Organisation"
},
"sameAs": [
"https://doi.org/10.1007/978-3-0348-9284-1_3",
"https://app.dimensions.ai/details/publication/pub.1045182218"
],
"sdDataset": "chapters",
"sdDatePublished": "2019-04-16T09:42",
"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/v90/0000000374_0000000374/records_119752_00000001.jsonl",
"type": "Chapter",
"url": "https://link.springer.com/10.1007%2F978-3-0348-9284-1_3"
}
]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.10.1007/978-3-0348-9284-1_3'
N-Triples is a line-based linked data format ideal for batch operations.
curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-0348-9284-1_3'
Turtle is a human-readable linked data format.
curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-0348-9284-1_3'
RDF/XML is a standard XML format for linked data.
curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-0348-9284-1_3'
This table displays all metadata directly associated to this object as RDF triples.
195 TRIPLES
23 PREDICATES
57 URIs
20 LITERALS
8 BLANK NODES