A Geometry for Multidimensional Integrable Systems [PDF]
, 1996 A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems.
Strachan, I. A. B.
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On the asymptotic expansion of certain plane singular integral operators
Boundary Value Problems, 2017 We discuss the problem of the asymptotic expansion for some operators in a general theory of pseudo-differential equations on manifolds with borders. Using the distribution theory one obtains certain explicit representations for these operators.
Vladimir Vasilyev
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Non-Hermitian von Roos Hamiltonian's $\eta$-weak-pseudo-Hermiticity, isospectrality and exact solvability [PDF]
, 2007 A complexified von Roos Hamiltonian is considered and a Hermitian first-order intertwining differential operator is used to obtain the related position dependent mass $\eta$-weak-pseudo-Hermitian Hamiltonians. Using a Liouvillean-type change of variables,
Bastard G +19 more
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Perturbation of an α-stable type stochastic process by a pseudo-gradient
Modern Stochastics: Theory and ApplicationsA Markov process defined by some pseudo-differential operator of an order $1\lt \alpha \lt 2$ as the process generator is considered. Using a pseudo-gradient operator, that is, the operator defined by the symbol $i\lambda |\lambda {|^{\beta -1}}$ with ...
Mykola Boiko, Mykhailo Osypchuk
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On the boundedness of periodic pseudo-differential operators
, 2017 In this paper we investigate the $L^p$-boundedness of certain classes of periodic pseudo-differential operators. The operators considered arise from the study of symbols on $\mathbb{T}^n\times\mathbb{Z}^n$ with limited regularity.Comment: Pseudo ...
Cardona, Duván
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On the singular integral representation of the fractional powers of Jacobi differential operators
AIMS MathematicsIn this paper, we introduce the fractional Jacobi operator and present its formulation in terms of a pseudo-differential operator via the Fourier–Jacobi transform.
Fethi Bouzeffour
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Isospectrality of spherical MHD dynamo operators: pseudo-Hermiticity and a no-go theorem
, 2002 The isospectrality problem is studied for the operator of the spherical hydromagnetic alpha^2-dynamo. It is shown that this operator is formally pseudo-Hermitian (J-symmetric) and lives in a Krein space.
Anderson +29 more
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Geometric approximations to transition densities of Jump-type Markov processes
Open Mathematics, 2021 This paper is concerned with the transition functions of symmetric Levy-type processes generated by a pseudo-differential operator with variable coefficients.
Zhuang Yuanying, Song Xiao
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The action of pseudo-differential operators on functions harmonic outside a smooth hyper-surface [PDF]
, 2012 We consider a smooth hyper-surface Z of a closed Riemannian manifold X. Let P be the Poisson operator associating to a smooth function on Z its harmonic extension on X\Z. If A is a pseudo-differential operator on X of degree
De Monvel, Louis Boutet +1 more
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On the Moyal quantized BKP type hierarchies
, 1997 Quantization of BKP type equations are done through the Moyal bracket and the formalism of pseudo-differential operators.
Faddeev L.D. +5 more
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