FUNCTIONAL LAPLACE OPERATOR ON A p-ADIC SPACE AND FEYNMAN-KAC AND FEYNMAN FORMULAS

被引：1

作者：

Shamarov, N. N. ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, NN Bogoliubov Inst Theoret Problems Microphys, Moscow 119899, Russia

来源：

VESTNIK SAMARSKOGO GOSUDARSTVENNOGO TEKHNICHESKOGO UNIVERSITETA-SERIYA-FIZIKO-MATEMATICHESKIYE NAUKI | 2011年 / 02期

关键词：

Feynman-Kac formulas; Feynman formulas; functional Laplacian; p-adic analysis;

D O I：

10.14498/vsgtu935

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Homogeneous closed PDO are constructed which are analogous to the powers of (absolute value of) infinite dimensional Laplacian and acting in Banach spaces of complex-valued functions defined on function spaces over a field of p-adic numbers. For elements of semigroups, for which these PDOs are generators, Feynman formulas and Feynman-Kac ones are obtained.

引用

页码：251 / 259

页数：9

共 19 条

[1] Feynman path integrals over p-adic vector space
Smolyanov, O. G.
Shamarov, N. N.
MATHEMATICAL MODELING OF WAVE PHENOMENA, 2009, 1106 : 286 - 297
[2] FEYNMAN FORMULAS FOR AN INFINITE-DIMENSIONAL p-ADIC HEAT TYPE EQUATION
Beloshapka, Olga
INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2011, 14 (01) : 137 - 148
[3] NONLINEAR FEYNMAN-KAC FORMULAS FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH SPACE-TIME NOISE
Song, Jian
Song, Xiaoming
Zhang, Qi
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2019, 51 (02) : 955 - 990
[4] THE FEYNMAN-KAC FORMULA AND HARNACK INEQUALITY FOR DEGENERATE DIFFUSIONS
Epstein, Charles L.
Pop, Camelia A.
ANNALS OF PROBABILITY, 2017, 45 (05) : 3336 - 3384
[5] Combining Continuous and Discrete Phenomena for Feynman's Operational Calculus in the Presence of a (C0) Semigroup and Feynman-Kac Formulas with Lebesgue-Stieltjes Measures
Nielsen, Lance
INTEGRAL EQUATIONS AND OPERATOR THEORY, 2018, 90 (01)
[6] Multilinear Hausdorff operator on p-adic functional spaces and its applications
Dao Van Duong
Ngo Thi Hong
ANALYSIS AND MATHEMATICAL PHYSICS, 2022, 12 (03)
[7] p-ADIC FRACTIONAL DIFFERENTIATION OPERATOR WITH POINT INTERACTIONS
Kuzhel, S.
Torba, S.
METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY, 2007, 13 (02): : 169 - 180
[8] p-adic Schrodinger-type operator with point interactions
Albeverio, S.
Kuzhel, S.
Torba, S.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 338 (02) : 1267 - 1281
[9] Minkowski Dimension and Explicit Tube Formulas for p-Adic Fractal Strings
Lapidus, Michel L.
Lu, Hung
van Frankenhuijsen, Machiel
FRACTAL AND FRACTIONAL, 2018, 2 (04) : 1 - 30
[10] A Note on Classical and p-adic Frechet Functional Equations with Restrictions
Almira, J. M.
RESULTS IN MATHEMATICS, 2013, 63 (1-2) : 649 - 656

← 1 2 →