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Dirichlet Problem for Poisson Equation on the Rectangle in Infinite Dimensional Hilbert Space


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Baker R. “Lebesgue measure” on R. Proceedings of the AMS. 113 (1991), no. 4., 1023–1029.BakerR“Lebesgue measure” on RProceedings of the AMS113199141023102910.2307/2048779Search in Google Scholar

V.M. Busovikov. Properties of one finite additive measure on lp invariant to shifts. Proceedings of MIPT. 10 (2018) no. 2. 163–172.BusovikovV.M.Properties of one finite additive measure on lp invariant to shiftsProceedings of MIPT1020182163172Search in Google Scholar

V.M. Busovikov, V.Zh. Sakbaev. Sobolev spaces of functions on Hilbert space with shift-invariant measure and approximation of semigroups. Izvestiya RAN. Ser. Mathematics. (2020) no. 4.BusovikovV.M.SakbaevV.Zh.Sobolev spaces of functions on Hilbert space with shift-invariant measure and approximation of semigroupsIzvestiya RAN. Ser. Mathematics2020410.1070/IM8890Search in Google Scholar

Ya. A. Butko. Chernoff approximation of subordinate semigroups. Stoch. Dyn. 1850021 (2017), 19 p., DOI: 10.1142/S0219493718500211.ButkoYa. A.Chernoff approximation of subordinate semigroupsStoch. Dyn185002120171910.1142/S0219493718500211Open DOISearch in Google Scholar

N. Dunford, J. Schwartz. Linear operators. General Theory. Moscow, 2004.DunfordN.SchwartzJ.Linear operators. General TheoryMoscow2004Search in Google Scholar

J.L. Lions, E. Magenes. Problems aux limites non homogenes et applications. Dunod, Paris, 1968.LionsJ.L.MagenesE.Problems aux limites non homogenes et applicationsDunod, Paris1968Search in Google Scholar

O.A. Oleynik. Lectures on the partial differential equations. Lomonosov MSU, Moscow, 2015.OleynikO.A.Lectures on the partial differential equationsLomonosov MSUMoscow2015Search in Google Scholar

I.D. Remizov, Formulas that represent Cauchy problem solution for momentum and position Schrodinger equation. Potential Anal (2018). https://doi.org/10.1007/s11118-018-9735-1RemizovI.D.Formulas that represent Cauchy problem solution for momentum and position Schrodinger equationPotential Anal2018https://doi.org/10.1007/s11118-018-9735-110.1007/s11118-018-9735-1Search in Google Scholar

I.D. Remizov, Explicit formula for evolution semigroup for diffusion in Hilbert space. Infinite Dimensional Analysis Quantum Probability and Related Topics (2018) Vol. 21, No. 04, 1850025.RemizovI.D.Explicit formula for evolution semigroup for diffusion in Hilbert spaceInfinite Dimensional Analysis Quantum Probability and Related Topics20182104185002510.1142/S021902571850025XSearch in Google Scholar

V.Zh. Sakbaev, Averaging of random walks and shift-invariant measures on a Hilbert space. Theoret. and Math. Phys. 191 (2017), no. 3., 886–909.SakbaevV.Zh.Averaging of random walks and shift-invariant measures on a Hilbert spaceTheoret. and Math. Phys1912017388690910.1134/S0040577917060083Search in Google Scholar

V.Zh. Sakbaev, Random walks and measures on Hilbert space that are invariant with respect to shifts and rotations. Differential equations. Mathematical physics. Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz. VINITI. 140 (2017), 88–118.SakbaevV.Zh.Random walks and measures on Hilbert space that are invariant with respect to shifts and rotationsDifferential equations. Mathematical physics. Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz. VINITI14020178811810.1007/s10958-019-04438-zSearch in Google Scholar

V.Zh. Sakbaev, Semigroups of operators in the space of function square integrable with respect to traslationary invariant measure on Banach space. Quantum probability. Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz. VINITI. 151 (2018), 73–90.SakbaevV.Zh.Semigroups of operators in the space of function square integrable with respect to traslationary invariant measure on Banach spaceQuantum probability. Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz. VINITI15120187390Search in Google Scholar

N.N. Shamarov, O.G. Smolyanov, Hamiltonian Feynman measures, Kolmogorov integral, and infinite-dimensional pseudodifferential operators Doklady Mathematics 100 (2019) no. 2., 445–449.ShamarovN.N.SmolyanovO.G.Hamiltonian Feynman measures, Kolmogorov integral, and infinite-dimensional pseudodifferential operatorsDoklady Mathematics1002019244544910.1134/S1064562419050120Search in Google Scholar

A.M. Vershik. Does There Exist a Lebesgue Measure in the Infinite-Dimensional Space? Proc. Steklov Inst. Math. 259 (2007), 248–272.VershikA.M.Does There Exist a Lebesgue Measure in the Infinite-Dimensional Space?Proc. Steklov Inst. Math259200724827210.1134/S0081543807040153Search in Google Scholar

D. V. Zavadsky, V. Zh. Sakbaev, Diffusion on a Hilbert Space Equipped with a Shift- and Rotation-Invariant Measure. Proc. Steklov Inst. Math., 306 (2019), 102–119.ZavadskyD. V.SakbaevV. Zh.Diffusion on a Hilbert Space Equipped with a Shift- and Rotation-Invariant MeasureProc. Steklov Inst. Math306201910211910.1134/S0081543819050109Search in Google Scholar

D.V. Zavadsky. Shift-invariant measures on sequence spaces// Proceedings of MIPT. 9 (2017), no. 4., 142–148.ZavadskyD.V.Shift-invariant measures on sequence spaces//Proceedings of MIPT920174142148Search in Google Scholar

D.V. Zavadsky, Analogs of Lebesgue measure on the sequences spaces and the classes of integrable functions. Quantum probability. Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz. VINITI. 151 (2018), 37–44.ZavadskyD.V.Analogs of Lebesgue measure on the sequences spaces and the classes of integrable functionsQuantum probability. Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz. VINITI15120183744Search in Google Scholar

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