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Keywords
(8)
banach space
Dual Space
gabor analysis
gabor transform
Lorentz Space
Modulation Space
Weight Function
Time Frequency
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Gabor analysis of the spaces M(p,q,w) (ℝ d) AND S(p,q,r,w,ω) (ℝ d)
Gabor analysis of the spaces M(p,q,w) (ℝ d) AND S(p,q,r,w,ω) (ℝ d),10.1016/S02529602(11)602166,Solidstate Electronics,Ayşi Sandikçi,A. Turan Gürkan
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Gabor analysis of the spaces M(p,q,w) (ℝ d) AND S(p,q,r,w,ω) (ℝ d)
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Ayşi Sandikçi
,
A. Turan Gürkanli
Let g be a nonzero rapidly decreasing function and w be a weight function. In this article in analog to modulation space, we define the space M(p,q,w) (ℝd) to be the subspace of tempered distributions f ɛ S'(ℝd) such that the
Gabor transform
Vg(f) of f is in the weighted
Lorentz space
L(p,q,wdμ)(ℝ2d). We endow this space with a suitable norm and show that it becomes a
Banach space
and invariant under time frequence shifts for 1≤p,q≤∞. We also investigate the embeddings between these spaces and the
dual space
of M(p,q,w)(ℝd). Later we define the space S(p,q,r,w,ω)ℝd for 1 <p < ∞, 1 ≤q ≤ ∞. We endow it with a sum norm and show that it becomes a Banach convolution algebra. We also discuss some properties of S(p,q,r,w,ω)(ℝd). At the end of this article, we characterize the multipliers of the spaces M(p,q,w)(ℝd) and S(p,q,r,w,ω)(ℝd).
Journal:
Solidstate Electronics  SOLID STATE ELECTRON
, vol. 31, no. 1, pp. 141158, 2011
DOI:
10.1016/S02529602(11)602166
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