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Abstract:

We show that coorbit spaces can be characterized in terms of arbitrary phase-space covers, which are families of phase-space multipliers associated with partitions of unity. This generalizes previously known results for time-frequency analysis to include time-scale decompositions. As a by-product, we extend the existing results for time-frequency analysis to an irregular setting. © 2011 Elsevier Inc.

Registro:

Documento: Artículo
Título:Characterization of coorbit spaces with phase-space covers
Autor:Romero, J.L.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, 1428 Capital Federal, Argentina
CONICET, Argentina
Palabras clave:Amalgam space; Coorbit theory; Localization operator; Phase-space localization; Wavelet transform
Año:2012
Volumen:262
Número:1
Página de inicio:59
Página de fin:93
DOI: http://dx.doi.org/10.1016/j.jfa.2011.09.005
Handle:http://hdl.handle.net/20.500.12110/paper_00221236_v262_n1_p59_Romero
Título revista:Journal of Functional Analysis
Título revista abreviado:J. Funct. Anal.
ISSN:00221236
CODEN:JFUAA
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00221236_v262_n1_p59_Romero.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221236_v262_n1_p59_Romero

Referencias:

  • Balan, R.M., Casazza, P.G., Heil, C., Landau, Z., Density, overcompleteness, and localization of frames I: Theory (2006) J. Fourier Anal. Appl., 12 (2), pp. 105-143
  • Baskakov, A.G., Wiener's theorem and the asymptotic estimates of the elements of inverse matrices (1990) Funct. Anal. Appl., 24 (3), pp. 222-224
  • Boggiatto, P., Localization operators with Lp symbols on modulation spaces (2004) Oper. Theory Adv. Appl., 155, pp. 149-163. , Birkhäuser, Basel, Advances in Pseudo-Differential Operators
  • Christensen, O., An Introduction to Frames and Riesz Bases (2003) Appl. Numer. Harmon. Anal., , Birkhäuser, Boston
  • Cordero, E., Gröchenig, K., Time-frequency analysis of localization operators (2003) J. Funct. Anal., 205 (1), pp. 107-131
  • Cordero, E., Gröchenig, K., Symbolic calculus and Fredholm property for localization operators (2006) J. Fourier Anal. Appl., 12 (3), pp. 371-392
  • Dahlke, S., Kutyniok, G., Steidl, G., Teschke, G., Shearlet coorbit spaces and associated Banach frames (2009) Appl. Comput. Harmon. Anal., 27 (2), pp. 195-214
  • Daubechies, I., Time-frequency localization operators: a geometric phase space approach (1988) IEEE Trans. Inform. Theory, 34 (4), pp. 605-612
  • Dörfler, M., Feichtinger, H.G., Gröchenig, K., Time-frequency partitions for the Gelfand triple (S0,L2,S0') (2006) Math. Scand., 98 (1), pp. 81-96
  • Dörfler, M., Gröchenig, K., Time-frequency partitions and characterizations of modulations spaces with localization operators (2011) J. Funct. Anal., 260 (7), pp. 1903-2190
  • Feichtinger, H.G., Banach convolution algebras of Wiener type (1983) Colloq. Math. Soc. Janos Bolyai, 35, pp. 509-524. , North-Holland, Amsterdam, B. Sz.-Nagy, J. Szabados (Eds.) Proc. Conf. on Functions, Series, Operators
  • Feichtinger, H.G., Banach spaces of distributions defined by decomposition methods. II (1987) Math. Nachr., 132, pp. 207-237
  • Feichtinger, H.G., Atomic characterizations of modulation spaces through Gabor-type representations (1989) Rocky Mountain J. Math., 19, pp. 113-126. , Proc. Conf. Constructive Function Theory
  • Feichtinger, H.G., Gröbner, P., Banach spaces of distributions defined by decomposition methods. I (1985) Math. Nachr., 123, pp. 97-120
  • Feichtinger, H.G., Gröchenig, K., Banach spaces related to integrable group representations and their atomic decompositions, I (1989) J. Funct. Anal., 86 (2), pp. 307-340
  • Feichtinger, H.G., Gröchenig, K., Banach spaces related to integrable group representations and their atomic decompositions, II (1989) Monatsh. Math., 108 (2-3), pp. 129-148
  • Feichtinger, H.G., Gröchenig, K., Gabor frames and time-frequency analysis of distributions (1997) J. Funct. Anal., 146 (2), pp. 464-495
  • Feichtinger, H.G., Nowak, K., A first survey of Gabor multipliers (2003) Appl. Numer. Harmon. Anal., pp. 99-128. , Birkhäuser, H.G. Feichtinger, T. Strohmer (Eds.) Advances in Gabor Analysis
  • Fendler, G., Gröchenig, K., Leinert, M., Symmetry of weighted l1-algebras and the GRS-condition (2006) Bull. Lond. Math. Soc., 38 (4), pp. 625-635
  • Fendler, G., Gröchenig, K., Leinert, M., Convolution-dominated operators on discrete groups (2008) Integral Equations Operator Theory, 61 (4), pp. 493-509
  • Fornasier, M., Gröchenig, K., Intrinsic localization of frames (2005) Constr. Approx., 22 (3), pp. 395-415
  • Fournier, J., Stewart, J., Amalgams of Lp and lq (1985) Bull. Amer. Math. Soc., 13 (1), pp. 1-21
  • Frazier, M., Jawerth, B., Decomposition of Besov spaces (1985) Indiana Univ. Math. J., 34, pp. 777-799
  • Frazier, M., Jawerth, B., A discrete transform and decompositions of distribution spaces (1990) J. Funct. Anal., 93 (1), pp. 34-170
  • Frazier, M.W., Jawerth, B.D., Weiss, G., (1991) Littlewood-Paley Theory and the Study of Function Spaces, , American Mathematical Society, Providence, RI
  • Führ, H., Abstract Harmonic Analysis of Continuous Wavelet Transforms (2005) Lecture Notes in Math., 1863. , Springer-Verlag
  • Gröchenig, K., Describing functions: atomic decompositions versus frames (1991) Monatsh. Math., 112 (3), pp. 1-41
  • Gröchenig, K., Foundations of Time-Frequency Analysis (2001) Appl. Numer. Harmon. Anal., , Birkhäuser Boston, Boston, MA
  • Gröchenig, K., Localization of frames, Banach frames, and the invertibility of the frame operator (2004) J. Fourier Anal. Appl., 10 (2), pp. 105-132
  • Gröchenig, K., Gabor frames without inequalities (2007) Int. Math. Res. Not. IMRN, 2007 (23), p. 21. , Art. ID rnm111
  • Gröchenig, K., Leinert, M., Wiener's lemma for twisted convolution and Gabor frames (2004) J. Amer. Math. Soc., 17, pp. 1-18
  • Gröchenig, K., Leinert, M., Symmetry and inverse-closedness of matrix algebras and symbolic calculus for infinite matrices (2006) Trans. Amer. Math. Soc., 358, pp. 2695-2711
  • Gröchenig, K., Piotrowski, M., Molecules in coorbit spaces and boundedness of operators (2009) Studia Math., 192 (1), pp. 61-77
  • Gröchenig, K., Toft, J., Isomorphism properties of Toeplitz operators in time-frequency analysis, , arxiv:0905.4954v2, preprint
  • Gromov, M., Groups of polynomial growth and expanding maps (1981) Publ. Math. Inst. Hautes Études Sci., 53 (1), pp. 53-78
  • He, Z., Wong, M., Localization operators associated to square integrable group representations (1996) Panamer. Math. J., 6 (1), pp. 93-104
  • Holland, F., Harmonic analysis on amalgams of Lp and ℓq (1975) J. Lond. Math. Soc., 10, pp. 295-305
  • Leptin, H., Poguntke, D., Symmetry and nonsymmetry for locally compact groups (1979) J. Funct. Anal., 33 (2), pp. 119-134
  • Liu, Y., Mohammed, A., Wong, M., Wavelet multipliers on Lp(Rn) (2008) Proc. Amer. Math. Soc., 136 (3), pp. 1009-1018
  • Luef, F., Projective modules over non-commutative tori are multi-window Gabor frames for modulation spaces (2009) J. Funct. Anal., 257 (6), pp. 1921-1946
  • Nashed, M., Sun, Q., Sampling and reconstruction of signals in a reproducing kernel subspace of Lp(Rd) (2010) J. Funct. Anal., 258 (7), pp. 2422-2452
  • Palmer, T., Classes of nonabelian, noncompact, locally compact groups (1978) Rocky Mountain J. Math., 8 (4), pp. 683-741
  • Romero, J.L., Surgery of spline-type and molecular frames (2011) J. Fourier Anal. Appl., 17 (1), pp. 135-174
  • Shin, C., Sun, Q., Stability of localized operators (2010) J. Funct. Anal., 258 (7), pp. 2422-2452
  • Sjöstrand, J., Wiener Type Algebras of Pseudodifferential Operators (1995) Sémin. Équ. Dériv. Partielles, 1994-1995, p. 21. , École Polytech, Palaiseau, Exp. No. IV
  • Sun, Q., Wiener's lemma for infinite matrices (2007) Trans. Amer. Math. Soc., 359 (7), p. 3099
  • Triebel, H., Theory of Function Spaces (1983) Monogr. Math., 78. , Birkhäuser, Basel
  • Triebel, H., Characterizations of Besov-Hardy-Sobolev spaces: A unified approach (1988) J. Approx. Theory, 52 (2), pp. 162-203
  • Ullrich, T., Continuous characterizations of Besov-Lizorkin-Triebel spaces and new interpretations as coorbits J. Funct. Spaces Appl., , arxiv:1007.3418v2, in press
  • Wong, M., Lp boundedness of localization operators associated to left regular representations (2002) Proc. Amer. Math. Soc., 130, pp. 2911-2919
  • Young, R.M., (2001) An Introduction to Nonharmonic Fourier Series, , Academic Press, Orlando, FL

Citas:

---------- APA ----------
(2012) . Characterization of coorbit spaces with phase-space covers. Journal of Functional Analysis, 262(1), 59-93.
http://dx.doi.org/10.1016/j.jfa.2011.09.005
---------- CHICAGO ----------
Romero, J.L. "Characterization of coorbit spaces with phase-space covers" . Journal of Functional Analysis 262, no. 1 (2012) : 59-93.
http://dx.doi.org/10.1016/j.jfa.2011.09.005
---------- MLA ----------
Romero, J.L. "Characterization of coorbit spaces with phase-space covers" . Journal of Functional Analysis, vol. 262, no. 1, 2012, pp. 59-93.
http://dx.doi.org/10.1016/j.jfa.2011.09.005
---------- VANCOUVER ----------
Romero, J.L. Characterization of coorbit spaces with phase-space covers. J. Funct. Anal. 2012;262(1):59-93.
http://dx.doi.org/10.1016/j.jfa.2011.09.005