Hamiltonian Feynman formulas for equations containing the vladimirov operator with variable coefficients

DOI10.1134/S1064562411060330zbMath1248.35242OpenAlexW2027434883MaRDI QIDQ653037

O. G. Smolyanov, N. N. Shamarov

Publication date: 6 January 2012

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562411060330

zbMATH Keywords

Cauchy problempseudodifferential operatorspartial differential equationsfunctional integrals\(p\)-adic fields

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Heat equation (35K05) (p)-adic and power series fields (11D88)

Related Items

Complete systems of eigenfunctions of the Vladimirov operator in \(L^2(B_r)\) and \(L^2(\mathbb{Q}_p)\), Solution of a Cauchy problem for a diffusion equation in a Hilbert space by a Feynman formula, The Method of Chernoff Approximation, Chernoff approximation of subordinate semigroups, Chernoff approximation for semigroups generated by killed Feller processes and Feynman formulae for time-fractional Fokker-Planck-Kolmogorov equations, Explicit formula for evolution semigroup for diffusion in Hilbert space

Cites Work

• Unnamed Item
• Unnamed Item
• Spectrum of a self-adjoint operator in \(L_ 2(K)\), where \(K\) is a local field; analog of the Feynman-Kac formula
• Feynman formulas for particles with position-dependent mass
• Feynman formulas and path integrals for evolution equations with the Vladimirov operator
• Dynamics on rugged landscapes of energy and ultrametric diffusion
• One-Parameter Semigroups for Linear Evolution Equations
• Statement of a Problem in Quantum Mechanics
• Space-Time Approach to Non-Relativistic Quantum Mechanics