Transformation semigroups of the space of functions that are square integrable with respect to a translation-invariant measure on a Banach space

DOI10.1007/s10958-020-05143-yzbMath1460.28010OpenAlexW3107924220MaRDI QIDQ2214368

V. Zh. Sakbaev

Publication date: 8 December 2020

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-020-05143-y

zbMATH Keywords

invariant measurerandom walkinfinitesimal generatorfinitely additive measurecontinuous one-parameter semigroup

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Schrödinger and Feynman-Kac semigroups (47D08)

Cites Work

• Notion of blowup of the solution set of differential equations and averaging of random semigroups
• On analogs of spectral decomposition of a quantum state
• Gaussian measures in Banach spaces
• Averaging of random walks and shift-invariant measures on a Hilbert space
• On the law of large numbers for compositions of independent random semigroups
• Does there exist a Lebesgue measure in the infinite-dimensional space?
• Self-adjoint approximations of the degenerate Schrödinger operator
• Geometric properties of systems of vector states and expansion of states in Pettis integrals
• Unbounded random operators and Feynman formulae
• "Lebesgue Measure" on R ∞
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