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330
Bilinear semi–classical moment functionals and their integral representation
 J. App. Theory
"... We introduce the notion of bilinear moment functional and study their general properties. The analogue of Favard’s theorem for moment functionals is proven. The notion of semiclassical bilinear functionals is introduced as a generalization of the corresponding notion for moment functionals and moti ..."
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Cited by 29 (15 self)
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We introduce the notion of bilinear moment functional and study their general properties. The analogue of Favard’s theorem for moment functionals is proven. The notion of semiclassical bilinear functionals is introduced as a generalization of the corresponding notion for moment functionals
ON THE PROPAGATION OF SEMICLASSICAL WIGNER FUNCTIONS
, 2001
"... Abstract. We establish the difference between the propagation of semiclassical Wigner functions and classical Liouville propagation. First we rediscuss the semiclassical limit for the propagator of Wigner functions, which on its own leads to their classical propagation. Then, via stationary phase e ..."
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Cited by 3 (0 self)
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evaluation of the full integral evolution equation, using the semiclassical expressions of Wigner functions, we provide the correct geometrical prescription for their semiclassical propagation. This is determined by the classical trajectories of the tips of the chords defined by the initial semiclassical
Bilinear summation formulas from quantum algebra representations
 Ramanujan J
"... Abstract. The tensor product of a positive and a negative discrete series representation of the quantum algebra Uq su(1,1) decomposes as a direct integral over the principal unitary series representations. Discrete terms can appear, and these terms are a finite number of discrete series representati ..."
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Cited by 11 (4 self)
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representations, or one complementary series representation. From the interpretation as overlap coefficients of little qJacobi functions and AlSalam and Chihara polynomials in base q and base q −1, two closely related bilinear summation formulas for the AlSalam and Chihara polynomials are derived. The formulas
INTEGRAL MOMENTS OF AUTOMORPHIC L–FUNCTIONS
"... Abstract. This paper exposes the underlying mechanism for obtaining second integral moments of GL2 automorphic L–functions over an arbitrary number field. Here, moments for GL2 are presented in a form enabling application of the structure of adele groups and their representation theory. To the best ..."
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Cited by 9 (3 self)
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Abstract. This paper exposes the underlying mechanism for obtaining second integral moments of GL2 automorphic L–functions over an arbitrary number field. Here, moments for GL2 are presented in a form enabling application of the structure of adele groups and their representation theory. To the best
Diffraction in the Semiclassical Approximation to Feynman’s Path Integral Representation of the Green
, 2008
"... We derive the semiclassical approximation to Feynman’s path integral representation of the energy Green function of a massless particle in the shadow region of an ideal obstacle in a medium. The wavelength of the particle is assumed to be comparable to or smaller than any relevant length of the prob ..."
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Cited by 1 (0 self)
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We derive the semiclassical approximation to Feynman’s path integral representation of the energy Green function of a massless particle in the shadow region of an ideal obstacle in a medium. The wavelength of the particle is assumed to be comparable to or smaller than any relevant length
Academy of Sciences, Kiev) GENERALIZED MOMENT REPRESENTATIONS AND PADÉ APPROXIMANTS ASSOCIATED WITH BILINEAR TRANSFORMATIONS
"... Using the method of generalized moment representations [1] with operator of bilinear transformation of independent variable Padé approximants of orders [N −1/N], N ≥ 1, are constructed for some special functions. 1 0. Introduction. V.K. Dzyadyk [1] in 1981 had proposed the method of generalized mome ..."
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Using the method of generalized moment representations [1] with operator of bilinear transformation of independent variable Padé approximants of orders [N −1/N], N ≥ 1, are constructed for some special functions. 1 0. Introduction. V.K. Dzyadyk [1] in 1981 had proposed the method of generalized
Semiclassical Series at Finite Temperature
, 1998
"... We derive the semiclassical series for the partition function of a onedimensional quantummechanical system consisting of a particle in a singlewell potential. We do this by applying the method of steepest descent to the pathintegral representation of the partition function, and we present a system ..."
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We derive the semiclassical series for the partition function of a onedimensional quantummechanical system consisting of a particle in a singlewell potential. We do this by applying the method of steepest descent to the pathintegral representation of the partition function, and we present a
Quantum Deformations of τfunctions,Bilinear Identities and Representation Theory 1
, 1994
"... This paper is a brief review of recent results on the concept of “generalized τfunction”, defined as a generating function of all the matrix elements in a given highestweight representation of a universal enveloping algebra G. Despite the differences from 1Talk presented at the Workshop on Symmetr ..."
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Cited by 1 (0 self)
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This paper is a brief review of recent results on the concept of “generalized τfunction”, defined as a generating function of all the matrix elements in a given highestweight representation of a universal enveloping algebra G. Despite the differences from 1Talk presented at the Workshop
SemiClassical Behavior of the Spectral Function 1
, 2005
"... We study the semiclassical behavior of the spectral function of the Schrödinger operator with short range potential. We prove that the spectral function is a semiclassical Fourier integral operator quantizing the forward and backward Hamiltonian flow relations of the system. Under a certain geometr ..."
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Cited by 2 (1 self)
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We study the semiclassical behavior of the spectral function of the Schrödinger operator with short range potential. We prove that the spectral function is a semiclassical Fourier integral operator quantizing the forward and backward Hamiltonian flow relations of the system. Under a certain
Real time correlation function in a single phase space integralbeyond the linearized semiclassical initial value representation
"... Abstract It is shown how quantum mechanical time correlation functions [defined, e.g., in Eq. (1.1)] can be expressed, without approximation, in the same form as the linearized approximation of the semiclassical initial value representation (LSCIVR), or classical Wigner model, for the correlation ..."
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Abstract It is shown how quantum mechanical time correlation functions [defined, e.g., in Eq. (1.1)] can be expressed, without approximation, in the same form as the linearized approximation of the semiclassical initial value representation (LSCIVR), or classical Wigner model, for the correlation
Results 1  10
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330