T-product of hypoelliptic operators

Maslov, V. P.; Shishmarev, I. A.

doi:10.1007/bf01084110

Cited by 3 publications

(3 citation statements)

References 4 publications

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“…The theorem can be proved by applying the theory of complex germ [2] and the results of [11][12][13][14][15] to problem (5), (3). The proof consists of the following stages.…”

Section: Theorem the Distribution ~ = K~x Ddd " 1 Is The Leadingmentioning

confidence: 99%

See 1 more Smart Citation

Random perturbations of invariant Lagrangian tori of Hamiltonian vector fields

Monvel¹,

Dobrokhotov

1998

Math Notes

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“…The theorem can be proved by applying the theory of complex germ [2] and the results of [11][12][13][14][15] to problem (5), (3). The proof consists of the following stages.…”

Section: Theorem the Distribution ~ = K~x Ddd " 1 Is The Leadingmentioning

confidence: 99%

“…The proof of the theorem is completed by estimating the difference between the exact and asymptotic solutions. The estimates can be obtained by using the results of [12,13]. [] The paper is devoted to the explicit calculation of the values of constantsthat appear in the stabilization theorem proved by the author in [1] (see also [21/.…”

Section: Lemmamentioning

confidence: 99%

Random perturbations of invariant Lagrangian tori of Hamiltonian vector fields

Monvel¹,

Dobrokhotov

1998

Math Notes

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“…An extensive advancement in the theory and applications of tropical mathematics was achieved by V. P. Maslov and his colleagues, who have introduced idempotent functional analysis as a new important field within the area. The results obtained by the Maslov scientific school and published in the monographs by Maslov and Samborskiȋ [20], Maslov and Kolokoltsov [21], Kolokoltsov and Maslov [22], as well as in many research papers, have provided a strong analytical framework for the contemporary tropical mathematics.…”

Section: Introductionmentioning

confidence: 99%

Algebraic solutions of tropical optimization problems

Krivulin

2015

Lobachevskii J Math

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We consider optimization problems that are formulated and solved in the framework of tropical mathematics. The problems consist in minimizing or maximizing functionals defined on vectors of finite-dimensional semimodules over idempotent semifields, and may involve constraints in the form of linear equations and inequalities. The objective function can be either a linear function or nonlinear function calculated by means of multiplicative conjugate transposition of vectors. We start with an overview of known tropical optimization problems and solution methods. Then, we formulate certain new problems and present direct solutions to the problems in a closed compact vector form suitable for further analysis and applications. For many problems, the results obtained are complete solutions.

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Time-ordered operators and Feynman–Dyson algebras

Gill

Zachary

1987

Journal of Mathematical Physics

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An approach to time-ordered operators based upon von Neumann's infinite tensor product Hilbert spaces is used to define Feynman-Dyson algebras. This theory is used to show that a one-to-one correspondence exists between path integrals and semi groups, which are integral operators defined by a kernel, the reproducing property of the kernel being a consequence of the semigroup property. For path integrals constructed from two semigroups, the results are more general than those obtained by the use of the Trotter-Kato formula. Perturbation series for the Feynman-Dyson operator calculus for time evolution and scattering operators are discussed, and it is pointed out that they are "asymptotic in the sense of Poincare" as defined in the theory of semi groups, thereby giving a precise formulation to a well-known conjecture of Dyson stated many years ago in the context of quantum electrodynamics. Moreover, the series converge when these operators possess suitable holomorphy properties.

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T-product of hypoelliptic operators

Cited by 3 publications

References 4 publications

Random perturbations of invariant Lagrangian tori of Hamiltonian vector fields

Random perturbations of invariant Lagrangian tori of Hamiltonian vector fields

Algebraic solutions of tropical optimization problems

Time-ordered operators and Feynman–Dyson algebras

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