Self-adjoint operators in the Smolyanov–Shamarov space.
Saved in:
| Title: | Self-adjoint operators in the Smolyanov–Shamarov space. |
|---|---|
| Authors: | Shelakov, M. G.1 (AUTHOR) shelakov.mikhail@mail.ru |
| Source: | Theoretical & Mathematical Physics. Apr2026, Vol. 227 Issue 1, p592-604. 13p. |
| Subjects: | Selfadjoint operators, Hilbert space, Function spaces, Lebesgue measure, Hilbert, David, 1862-1943, Fourier transforms, Laplacian operator |
| Abstract: | We prove the essential self-adjointness of the Laplace–Volterra operator in the Smolyanov–Shamarov space, i.e., in the space of functions defined on a real infinite-dimensional separable Hilbert space and square-integrable with respect to a generalized Lebesgue–Feynman–Smolyanov–Shamarov measure. To prove this, we first prove the essential self-adjointness of the operator of multiplication by a quadratic function with a kernel operator. Then we apply the infinite-dimensional Fourier transform, mapping functions from an infinite-dimensional analogue of the Schwartz space to functions from the same space. Furthermore, a consequence of one of the proved theorems is the separability of the Smolyanov–Shamarov space. [ABSTRACT FROM AUTHOR] |
| Copyright of Theoretical & Mathematical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 193198531 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Self-adjoint operators in the Smolyanov–Shamarov space. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Shelakov%2C+M%2E+G%2E%22">Shelakov, M. G.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> shelakov.mikhail@mail.ru</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Theoretical+%26+Mathematical+Physics%22">Theoretical & Mathematical Physics</searchLink>. Apr2026, Vol. 227 Issue 1, p592-604. 13p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Selfadjoint+operators%22">Selfadjoint operators</searchLink><br /><searchLink fieldCode="DE" term="%22Hilbert+space%22">Hilbert space</searchLink><br /><searchLink fieldCode="DE" term="%22Function+spaces%22">Function spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Lebesgue+measure%22">Lebesgue measure</searchLink><br /><searchLink fieldCode="DE" term="%22Hilbert%2C+David%2C+1862-1943%22">Hilbert, David, 1862-1943</searchLink><br /><searchLink fieldCode="DE" term="%22Fourier+transforms%22">Fourier transforms</searchLink><br /><searchLink fieldCode="DE" term="%22Laplacian+operator%22">Laplacian operator</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We prove the essential self-adjointness of the Laplace–Volterra operator in the Smolyanov–Shamarov space, i.e., in the space of functions defined on a real infinite-dimensional separable Hilbert space and square-integrable with respect to a generalized Lebesgue–Feynman–Smolyanov–Shamarov measure. To prove this, we first prove the essential self-adjointness of the operator of multiplication by a quadratic function with a kernel operator. Then we apply the infinite-dimensional Fourier transform, mapping functions from an infinite-dimensional analogue of the Schwartz space to functions from the same space. Furthermore, a consequence of one of the proved theorems is the separability of the Smolyanov–Shamarov space. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Theoretical & Mathematical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=193198531 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1134/S0040577926040021 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 13 StartPage: 592 Subjects: – SubjectFull: Selfadjoint operators Type: general – SubjectFull: Hilbert space Type: general – SubjectFull: Function spaces Type: general – SubjectFull: Lebesgue measure Type: general – SubjectFull: Hilbert, David, 1862-1943 Type: general – SubjectFull: Fourier transforms Type: general – SubjectFull: Laplacian operator Type: general Titles: – TitleFull: Self-adjoint operators in the Smolyanov–Shamarov space. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Shelakov, M. G. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 04 Text: Apr2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00405779 Numbering: – Type: volume Value: 227 – Type: issue Value: 1 Titles: – TitleFull: Theoretical & Mathematical Physics Type: main |
| ResultId | 1 |
