Hamiltonian Feynman Measures, Kolmogorov Integral, and Infinite-Dimensional Pseudodifferential Operators

O. G. Smolyanov; N. N. Shamarov

doi:10.1134/S1064562419050120

Hamiltonian Feynman Measures, Kolmogorov Integral, and Infinite-Dimensional Pseudodifferential Operators

Authors: Smolyanov O.G.¹^,2, Shamarov N.N.¹^,2
Affiliations:
1. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University
2. Moscow Institute of Physics and Technology (State University)
Issue: Vol 100, No 2 (2019)
Pages: 445-449
Section: Mathematics
URL: https://journals.rcsi.science/1064-5624/article/view/225717
DOI: https://doi.org/10.1134/S1064562419050120
ID: 225717

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Abstract

Properties of infinite-dimensional pseudodifferential operators (PDO) are discussed. In particular, the connection between two definitions of PDO is considered: one given in terms of the Hamiltonian Feynman measure and the other introduced in this work in terms of the Kolmogorov integral.

About the authors

O. G. Smolyanov

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University; Moscow Institute of Physics and Technology (State University)

Author for correspondence.
Email: smolyanov@yandex.ru
Russian Federation, Moscow, 119991; Dolgoprudnyi, Moscow oblast, 141700

N. N. Shamarov

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University; Moscow Institute of Physics and Technology (State University)

Author for correspondence.
Email: nshamarov@yandex.ru
Russian Federation, Moscow, 119991; Dolgoprudnyi, Moscow oblast, 141700

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