Weyl-Heisenberg frame in p-adic analysis

Analyzing the Weyl-heisenberg Frame Identity

In 1990, Daubechies proved a fundamental identity for WeylHeisenberg systems which is now called the Weyl-Heisenberg Frame Identity. WH-Frame Identity: If g ∈ W (L∞, L), then for all continuous, compactly supported functions f we have: ∑ m,n | < f, EmbTnag > | = 1 b ∑

A Necessary Condition for Weyl-Heisenberg Frames

Roots of Complex Polynomials and Weyl-heisenberg Frame Sets

A Weyl-Heisenberg frame for L2(R) is a frame consisting of modulates Embg(t) = e 2πimbtg(t) and translates Tnag(t) = g(t − na), m,n ∈ Z, of a fixed function g ∈ L2(R), for a, b ∈ R. A fundamental question is to explicitly represent the families (g, a, b) so that (EmbTnag)m,n∈Z is a frame for L2(R). We will show an interesting connection between this question and a classical problem of Littlewoo...

Discrete Weyl–Heisenberg transforms

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Quantum Heisenberg–Weyl Algebras

All Lie bialgebra structures on the Heisenberg–Weyl algebra [A+, A−] = M are classified and explicitly quantized. The complete list of quantum Heisenberg–Weyl algebras so obtained includes new multiparameter deformations, most of them being of the non-coboundary type. A Hopf algebra deformation of a universal enveloping algebra Ug defines in a unique way a Lie bialgebra structure (g, δ) on g [1...