A wavelet theory for local fields and related groups

Benedetto, John J.; Benedetto, Robert L.

doi:10.1007/bf02922099

Cited by 154 publications

(130 citation statements)

References 54 publications

(77 reference statements)

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“…Consider the 3-adic group Q 3 with compact open subgroup Z 3 . If V 1 = 3Z 3 , V 2 = 1 + 3Z 3 and V 3 = 2 + 3Z 3 , then {V i ; i = 1, 2, 3} is a partition for Z 3 [3].…”

Section: Theorem 24 We Assume That X = {τ [S] ϕ; ϕ ∈ φ [S] ∈ G/h}mentioning

confidence: 99%

Shift Generated Dual Frames for Locally Compact Abelian Groups

Ahmadi¹,

Hemmat²

2012

Journal of the Korean Mathematical Society

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Abstract. Let G be a metrizable, σ-compact locally compact abelian group with a compact open subgroup. In this paper we define the Gramian and the dual Gramian operators for shift invariant subspaces of L 2 (G) and we use them to characterize shift generated dual frames for shift invariant spaces, which forms a frame for a subspace of L 2 (G). We present necessary and sufficient conditions for which standard dual is a unique SG-dual frame of type I and type II.

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“…Consider the 3-adic group Q 3 with compact open subgroup Z 3 . If V 1 = 3Z 3 , V 2 = 1 + 3Z 3 and V 3 = 2 + 3Z 3 , then {V i ; i = 1, 2, 3} is a partition for Z 3 [3].…”

Section: Theorem 24 We Assume That X = {τ [S] ϕ; ϕ ∈ φ [S] ∈ G/h}mentioning

confidence: 99%

Shift Generated Dual Frames for Locally Compact Abelian Groups

Ahmadi¹,

Hemmat²

2012

Journal of the Korean Mathematical Society

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“…Кон-струкция p-адических всплесков была обобщена Бенедетто и Бе-недетто [118], [117] на некоторый класс абелевых локально ком-пактных групп. Новые примеры p-адических всплесков были вве-дены в [242], [90], [184].…”

Section: библиографический обзорunclassified

Untitled

Козырев¹

2008

Sovrem. Probl. Mat.

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“…By choosing Ψ , B, and A appropriately, one can make G B (Ψ ) and W A (Ψ ) an orthonormal basis or, more generally, a Parseval frame for L 2 (R n ) (defined below). While the theory of Gabor and affine systems has usually been developed on R n , there is an increasing interest in the study of these systems in other settings (for example, [1,8,12,16]). Indeed, discrete signal processing applications, as well as numerical implementations of these theories, require the construction of reproducing systems on Z n or finite abelian groups.…”

mentioning

confidence: 99%