Расширения Пространств С Цилиндрическими Мерами И Носители Мер, Порождаемых Лапласианом Леви

Смолянов, Олег Георгиевич; Smolyanov, O. G.; Аккарди, Луиджи; Accardi, Luigi

doi:10.4213/mzm1423

Mat. Zametki

1998

DOI: 10.4213/mzm1423

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Расширения Пространств С Цилиндрическими Мерами И Носители Мер, Порождаемых Лапласианом Леви

Олег Георгиевич Смолянов¹,

O. G. Smolyanov²,

Луиджи Аккарди³

et al.

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Feynman formulas for evolution equations with Levy Laplacians on infinite-dimensional manifolds

Accardi

Smolyanov

2006

Dokl. Math.

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A Feynman formula is a representation of the solution\ud to the Cauchy problem for an evolution partial differential\ud (or pseudodifferential) equation in terms of the\ud limit of a sequence of multiple integrals with multiplicities\ud tending to infinity. The integrands are products of\ud the initial condition and Gaussian (or complex Gaussian)\ud exponentials\ud 1\ud [5]. In this paper, we obtain Feynman\ud formulas for the solutions to the Cauchy problems\ud for the Schrödinger equation and the heat equation with\ud Levy Laplacian on the infinite-dimensional manifold of\ud mappings from a closed real interval to a Riemannian\ud manifold. The definition of the Levi Laplacian acting\ud on functions on such a manifold is obtained by combining\ud the methods of papers [3] and [7]. In the former,\ud Levi Laplacians in the space of functions on an infinitedimensional\ud vector space were considered, and in the\ud latter, Volterra Laplacians in the space of functions on\ud the above infinite-dimensional manifold were examined.\ud This definition of a Levi Laplacian is equivalent to\ud that given in [2], but it i

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Feynman formulas for evolution equations with Levy Laplacians on infinite-dimensional manifolds

Accardi

Smolyanov

2006

Dokl. Math.

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Generalized Lévy Laplacians and Cesàro means

Accardi

Smolyanov

2009

Dokl. Math.

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Связь Между Различными Реализациями Преобразований Боголюбова

Tveritinov¹

2004

Mat. Zametki

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Расширения Пространств С Цилиндрическими Мерами И Носители Мер, Порождаемых Лапласианом Леви

Cited by 4 publications

References 0 publications

Feynman formulas for evolution equations with Levy Laplacians on infinite-dimensional manifolds

Feynman formulas for evolution equations with Levy Laplacians on infinite-dimensional manifolds

Generalized Lévy Laplacians and Cesàro means

Связь Между Различными Реализациями Преобразований Боголюбова

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