Bibliographic Details
| 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] |
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| Database: |
Engineering Source |
