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INTEGRALS OF PRODUCTS OF HERMITE FUNCTIONS
, 901
"... Abstract. We compute the integrals of products of Hermite functions using the generating functions. The precise asymptotics of products of 4 Hermite functions are presented below. This estimate is relevant for the corresponding cubic nonlinear equation. ..."
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Abstract. We compute the integrals of products of Hermite functions using the generating functions. The precise asymptotics of products of 4 Hermite functions are presented below. This estimate is relevant for the corresponding cubic nonlinear equation.
Gabor (Super)Frames with Hermite Functions
 Math. Annalen
"... Abstract. We investigate vectorvalued Gabor frames (sometimes called Gabor superframes) based on Hermite functions Hn. Let h = (H0, H1,..., Hn) be the vector of the first n + 1 Hermite functions. We give a complete characterization of all lattices Λ ⊆ R 2 such that the Gabor system {e 2πiλ2t h(t − ..."
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Cited by 16 (0 self)
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Abstract. We investigate vectorvalued Gabor frames (sometimes called Gabor superframes) based on Hermite functions Hn. Let h = (H0, H1,..., Hn) be the vector of the first n + 1 Hermite functions. We give a complete characterization of all lattices Λ ⊆ R 2 such that the Gabor system {e 2πiλ2t h
Asymptotic coefficients of Hermite function series
 J. Comput. Phys
, 1984
"... By using complex variable methods (steepest descent and residues) to asymptotically evaluate the coefftcient integrals, the numerical analysis of Hermite function series is discussed. There are striking similarities and differences with the author’s earlier work on Chebyshev polynomial methods (J. C ..."
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Cited by 10 (0 self)
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By using complex variable methods (steepest descent and residues) to asymptotically evaluate the coefftcient integrals, the numerical analysis of Hermite function series is discussed. There are striking similarities and differences with the author’s earlier work on Chebyshev polynomial methods (J
Spectral and pseudospectral approximations using Hermite functions: . . .
, 2003
"... We consider in this paper spectral and pseudospectral approximations using Hermite functions for PDEs on the whole line. We first develop some basic approximation results associated with the projections and interpolations in the spaces spanned by Hermite functions. These results play important roles ..."
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Cited by 15 (5 self)
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We consider in this paper spectral and pseudospectral approximations using Hermite functions for PDEs on the whole line. We first develop some basic approximation results associated with the projections and interpolations in the spaces spanned by Hermite functions. These results play important
MULTICARRIER SIGNAL SHAPING EMPLOYING HERMITE FUNCTIONS
"... In this paper, we introduce a novel signal shaping approach for multicarrier systems. We propose to combine Hermite functions in order to get a good timefrequency localization property for multicarrier signals, which is important for robustness against the timefrequency dispersion of the wireles ..."
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Cited by 1 (0 self)
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In this paper, we introduce a novel signal shaping approach for multicarrier systems. We propose to combine Hermite functions in order to get a good timefrequency localization property for multicarrier signals, which is important for robustness against the timefrequency dispersion
A note on reassigned Gabor spectrograms of Hermite functions
, 2012
"... An explicit form is given for the reassigned Gabor spectrogram of an Hermite function of arbitrary order. It is shown that the energy concentration sharply localizes outside the border of a clearance area limited by the “classical ” circle where the Gabor spectrogram attains its maximum value, with ..."
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Cited by 1 (0 self)
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An explicit form is given for the reassigned Gabor spectrogram of an Hermite function of arbitrary order. It is shown that the energy concentration sharply localizes outside the border of a clearance area limited by the “classical ” circle where the Gabor spectrogram attains its maximum value
Clustering ECG complexes using Hermite functions and selforganizing maps
 IEEE Trans. Biomed. Eng
, 2000
"... Abstract—An integrated method for clustering of QRS complexes is presented which includes basis function representation and selforganizing neural networks (NN’s). Each QRS complex is decomposed into Hermite basis functions and the resulting coefficients and width parameter are used to represent the ..."
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Cited by 45 (1 self)
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Abstract—An integrated method for clustering of QRS complexes is presented which includes basis function representation and selforganizing neural networks (NN’s). Each QRS complex is decomposed into Hermite basis functions and the resulting coefficients and width parameter are used to represent
Hermite Functions And Uncertainty Principles For The Fourier And The Windowed Fourier Transforms
 Rev. Mat. Iberoamericana
"... We extend an uncertainty principle due to Beurling into a characterization of Hermite functions. More precisely, all functions f on R which may be written as P (x) exp(Ax; x), with A a real symmetric de nite positive matrix, are characterized by integrability conditions on the product f(x) f(y) ..."
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Cited by 34 (4 self)
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We extend an uncertainty principle due to Beurling into a characterization of Hermite functions. More precisely, all functions f on R which may be written as P (x) exp(Ax; x), with A a real symmetric de nite positive matrix, are characterized by integrability conditions on the product f(x) f
Grounding in communication
 In
, 1991
"... We give a general analysis of a class of pairs of positive selfadjoint operators A and B for which A + XB has a limit (in strong resolvent sense) as h10 which is an operator A, # A! Recently, Klauder [4] has discussed the following example: Let A be the operator(d2/A2) + x2 on L2(R, dx) and let ..."
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Cited by 1082 (19 self)
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B = 1 x 1s. The eigenvectors and eigenvalues of A are, of course, well known to be the Hermite functions, H,(x), n = 0, l,... and E, = 2n + 1. Klauder then considers the eigenvectors of A + XB (A> 0) by manipulations with the ordinary differential equation (we consider the domain questions
Results 1  10
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41,207