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Perturbations of WeylHeisenberg frames
 MR 2003h:42048
"... Abstract. We develop a usable perturbation theory for WeylHeisenberg frames. In particular, we prove that if (EmbTnag)m,n∈Z is a WHframe and h is a function which is close to g in the Wiener Amalgam space norm, then also (EmbTnah)m,n∈Z is a WHframe. We also prove perturbation results for the para ..."
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Cited by 2 (0 self)
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Abstract. We develop a usable perturbation theory for WeylHeisenberg frames. In particular, we prove that if (EmbTnag)m,n∈Z is a WHframe and h is a function which is close to g in the Wiener Amalgam space norm, then also (EmbTnah)m,n∈Z is a WHframe. We also prove perturbation results
Lattice Tiling and the WeylHeisenberg Frames
 Geom. Funct. Anal
, 2000
"... Let L and K be two full rank lattices in R d . We prove that if v(L) = v(K), i.e. they have the same volume, then there exists a measurable set such that it tiles R d by both L and K. A counterexample shows that the above tiling result is false for three or more lattices. Furthermore, we prove ..."
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Cited by 26 (3 self)
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prove that if v(L) v(K) then there exists a measurable set such that it tiles by L and packs by K. Using these tiling results we answer a well known question on the density property of WeylHeisenberg frames. 1991 Mathematics Subject Classication. Primary 52C22, 52C17, 42B99, 42C30. Key words
An Introduction to Irregular WeylHeisenberg Frames
"... ABSTRACT We give an introduction to irregular WeylHeisenberg frames showing the latest developments and open problems. We provide several new results for semiirregular ..."
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Cited by 1 (0 self)
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ABSTRACT We give an introduction to irregular WeylHeisenberg frames showing the latest developments and open problems. We provide several new results for semiirregular
Tight WeylHeisenberg Frames in l²(Z)
 IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 1998
"... Tight WeylHeisenberg frames in l²(Z) are the tool for shorttime Fourier analysis in discrete time. They are closely related to paraunitary modulated filter banks and are studied here using techniques of the filter bank theory. Good resolution of shorttime Fourier analysis in the joint timefrequ ..."
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Tight WeylHeisenberg frames in l²(Z) are the tool for shorttime Fourier analysis in discrete time. They are closely related to paraunitary modulated filter banks and are studied here using techniques of the filter bank theory. Good resolution of shorttime Fourier analysis in the joint time
Roots of complex polynomials and WeylHeisenberg frame sets
 Proc. Amer. Math. Soc
"... Abstract. A WeylHeisenberg frame for L2 (R) is a frame consisting of modulates Embg(t) =e2πimbtg(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) sothat(EmbTnag)m,n∈Z is a frame for ..."
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Cited by 13 (3 self)
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Abstract. A WeylHeisenberg frame for L2 (R) is a frame consisting of modulates Embg(t) =e2πimbtg(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) sothat(EmbTnag)m,n∈Z is a frame
From WeylHeisenberg Frames to Infinite Quadratic Forms
, 2008
"... Let a, b be two fixed positive constants. A function g ∈ L 2 (R) is called a mother WeylHeisenberg frame wavelet for (a,b) if g generates a frame for L 2 (R) under modulates by b and translates by a, i.e., {e imbt g(t− na}m,n∈Z is a frame for L 2 (R). In this paper, we establish a connection betwee ..."
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between mother WeylHeisenberg frame wavelets of certain special forms and certain strongly positive definite quadratic forms of infinite dimension. Some examples of application in matrix algebra are provided. 1
Lammers Bracket products for WeylHeisenberg frames Preprint
"... Abstract. We provide a detailed development of a function valued inner product known as the bracket product and used effectively by de Boor, Devore, Ron and Shen to study translation invariant systems. We develop a version of the bracket product specifically geared to WeylHeisenberg frames. This br ..."
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Cited by 9 (2 self)
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Abstract. We provide a detailed development of a function valued inner product known as the bracket product and used effectively by de Boor, Devore, Ron and Shen to study translation invariant systems. We develop a version of the bracket product specifically geared to WeylHeisenberg frames
Results 1  10
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677,337