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Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms.

Aline Bonami, Demange, Bruno, Jaming, Philippe (2003)

Revista Matemática Iberoamericana

We extend an uncertainty principle due to Beurling into a characterization of Hermite functions. More precisely, all functions f on Rd which may be written as P(x)exp(-(Ax,x)), with A a real symmetric definite positive matrix, are characterized by integrability conditions on the product f(x)f(y). We then obtain similar results for the windowed Fourier transform (also known, up to elementary changes of functions, as the radar ambiguity function or the Wigner transform). We complete the paper with...

Hermite Series with Polar Singularities

Boychev, Georgi S. (2012)

Mathematica Balkanica New Series

MSC 2010: 33C45, 40G05Series in Hermite polynomials with poles on the boundaries of their regions of convergence are considered.

Hilbert series of the Grassmannian and k -Narayana numbers

Lukas Braun (2019)

Communications in Mathematics

We compute the Hilbert series of the complex Grassmannian using invariant theoretic methods. This is made possible by showing that the denominator of the q -Hilbert series is a Vandermonde-like determinant. We show that the h -polynomial of the Grassmannian coincides with the k -Narayana polynomial. A simplified formula for the h -polynomial of Schubert varieties is given. Finally, we use a generalized hypergeometric Euler transform to find simplified formulae for the k -Narayana numbers, i.e. the h -polynomial...

Homology for irregular connections

Spencer Bloch, Hélène Esnault (2004)

Journal de Théorie des Nombres de Bordeaux

Homology with values in a connection with possibly irregular singular points on an algebraic curve is defined, generalizing homology with values in the underlying local system for a connection with regular singular points. Integration defines a perfect pairing between de Rham cohomology with values in the connection and homology with values in the dual connection.

Hurwitz continued fractions with confluent hypergeometric functions

Takao Komatsu (2007)

Czechoslovak Mathematical Journal

Many new types of Hurwitz continued fractions have been studied by the author. In this paper we show that all of these closed forms can be expressed by using confluent hypergeometric functions 0 F 1 ( ; c ; z ) . In the application we study some new Hurwitz continued fractions whose closed form can be expressed by using confluent hypergeometric functions.

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