Solving evolution equations (heat-type and Schrödinger-type) equations via Feynman formulas, quasi-Feynman integral formulas and formulas obtained via the shift operator
Feynman and quasi-Feynman integral formulas
Main publications:
Sonia Mazzucchi, Valter Moretti, Ivan Remizov, Oleg Smolyanov, “Chernoff approximations of Feller semigroups in Riemannian manifolds”, Mathematische Nachrichten, 296:3 (2023), 1244-1284 , arXiv: https://arxiv.org/abs/2002.06606
I.D.Remizov, “Formulas that represent Cauchy problem solution for momentum and position Schrödinger equation”, Potential Analysis, 52 (2020), 339–370https://link.springer.com/article/10.1007
Ivan D. Remizov, “Solution-giving formula to Cauchy problem for multidimensional parabolic equation with variable coefficients”, Journal of Mathematical Physics, 60:7 (2019), 071505https://aip.scitation.org/doi/10.1063/1.5038102
I.D.Remizov, “Explicit formula for evolution semigroup for diffusion in Hilbert space”, Infinite Dimensional Analysis, Quantum Probability and Related Topics, 21:4 (2018), 1850025 , 35 pp. https://doi.org/10.1142/S021902571850025X
I. D. Remizov, “Feynman and Quasi-Feynman Formulas for Evolution Equations”, Doklady Mathematics, 96:2 (2017), 433–437
Ivan D. Remizov, “Quasi-Feynman formulas – a method of obtaining the evolution operator for the Schrödinger equation”, Journal of Functional Analysis, 270:12 (2016), 4540-4557 , arXiv: 1409.8345
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