Abstract:It is well known that the Gabor expansions converge to identity operator in
weak* sense on the Wiener amalgam spaces as sampling density tends to infinity.
In this paper we prove the convergence of Gabor expansions to identity operator
in the operator norm as well as weak* sense on $W(L^p, \ell^q)$ as the sampling
density tends to infinity. Also we show the validity of the Janssen's
representation and the Wexler-Raz biorthogonality condition for Gabor frame
operator on $W(L^p, \ell^q)$.Comment: 16 page
In this paper we establish Parseval type identities and surprising new inequalities for Hilbert-Schmidt frames. Our results generalize and improve the remarkable results which have been obtained by Balan et al. and Gȃvruţa.The constants A and B are called f rame bounds. If A = B, then this frame is called anA-tight f rame, and if A = B = 1, then it is called a P arseval f rame.
In this paper we establish Parseval type identities and surprising new inequalities for Hilbert-Schmidt frames. Our results generalize and improve the remarkable results which have been obtained by Balan et al. and Gȃvruţa.The constants A and B are called f rame bounds. If A = B, then this frame is called anA-tight f rame, and if A = B = 1, then it is called a P arseval f rame.
“…The constants A and B are called lower and upper frame bounds. We refer to [14,22,26] for basic results on frames and [3,23,28,31] for generalizations of frames.…”
Abstract. In this paper we study the Hilbert−Schmidt frame (HS-frame) theory for separable Hilbert spaces. We first present some characterizations of HS-frames and prove that HS-frames share many important properties with frames. Then we show how the inverse of the HS-frame operator can be approximated using finite-dimensional methods. Finally we present a classical perturbation result and prove that HS-frames are stable under small perturbations.
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