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A unified approach to atomic decompositions via integrable group representations

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References

  1. J.B. ALLEN, L.R. RABINER: A unified approach to short-time Fourier analysis and synthesis. Proc. IEEE, Vol. 65/11, 1558–1564 (1977).

    Article  Google Scholar 

  2. J. ARAZY, S.D. FISHER, J. PEETRE: Möbius invariant function spaces. J.Reine Angew.Math. 263, 110–145 (1986).

    MathSciNet  Google Scholar 

  3. J.ARAZY, S.D.FISHER, J.PEETRE: Hankel operators on weighted Bergman spaces. Preprint Sept. 1986.

    Google Scholar 

  4. L. AUSLANDER, R. TOLIMIERI: Radar ambiguity functions and group theory. SIAM J. Math. Anal. 16, 577–601 (1985).

    Article  MATH  MathSciNet  Google Scholar 

  5. M.J.BASTIAANS: Signal description by means of local frequency spectrum. SPIE Vol.373, Transformation in optical signal processing, 49–62 (1981).

    Google Scholar 

  6. A. BENEDEK, R. PANZONE: The spaces Lp, with mixed norm. Duke Math. J. 28, 303–324 (1961).

    Article  MathSciNet  Google Scholar 

  7. J. BERGH, J. LÖFSTRÖM: Interpolation Spaces (An Introduction), Grundl.math.Wiss. 223, Berlin-Heidelberg-New York, Springer, 1976.

    Book  Google Scholar 

  8. R.C. BUSBY, H.A. SMITH: Product-convolution operators and mixed norm spaces. Trans.Amer.Math.Soc. 263, 309–341 (1981).

    Article  MATH  MathSciNet  Google Scholar 

  9. A.L. CAREY: Square-integrable representations of non-unimodular groups. Bull.Austral.Math.Soc. 15, 1–12 (1976).

    Article  MATH  MathSciNet  Google Scholar 

  10. T. CLAASEN, W. MECKLENBRÄUCKER: The Wigner distribution — a tool for time-frequency signal analysis. I–III. Philips J.Res.35, 217–250, 276–300, and 372–389 (1980).

    MATH  MathSciNet  Google Scholar 

  11. R. COIFMAN, R. ROCHBERG: Representation theorems for holomorphic and harmonic functions. Astérisque 77, 11–65 (1980).

    MATH  MathSciNet  Google Scholar 

  12. I. DAUBECHIES, A. GROSSMANN, Y. MEYER: Painless nonorthogonal expansions. J.Math.Phys. 27, 1271–1283 (1986).

    Article  MATH  MathSciNet  Google Scholar 

  13. M. DUFLO, C.C. MOORE: On the regular representation of a non unimodular locally compact group. J.Functional Anal.21, 209–243 (1976).

    Article  MATH  MathSciNet  Google Scholar 

  14. P.EYMARD, M.TERP: La transformation de Fourier et son inverse sur le groupe des ax+b d’un corps local. In "Analyse Harmonique sur les Groupes de Lie II", pp.207–248, Lect.Notes in Math. 739, Springer. 1979.

    Google Scholar 

  15. H.G. FEICHTINGER: Banach convolution algebras of Wiener’s type. "Functions, Series, Operators", Proc.Conf., Budapest 1980, Coll. Soc. Janos Bolyai, North Holland, Amsterdam (1983), 509–524.

    Google Scholar 

  16. —: Banach spaces of distributions of Wiener’s type and interpolation. "Functional Analysis and Approximation", Proc. Conf., Oberwolfach 1980, Ed. P.Butzer, B Sz.Nagy and E.Görlich, Birkhäuser-Verlag, ISNM 60, (1981), 153–165.

    Google Scholar 

  17. —: On a new Segal algebra. Monatsh.Math. 92, 269–289 (1981).

    Article  MATH  MathSciNet  Google Scholar 

  18. —: Un espace de Banach de distributions tempérées sur les groupes localement compacts abéliens. C.R.Acad.Sci. Paris, Sér A 290, no.17, 791–794(1980).

    MATH  MathSciNet  Google Scholar 

  19. —: Gewichtsfunktionen auf lokalkompakten Gruppen, Sitzber. Österr. Akad.Wiss,Abt.II,Bd.188 (1979),451–471.

    MATH  MathSciNet  Google Scholar 

  20. —:Modulation spaces on locally compact abelian groups, Techn.Report, Vienna, 1983.

    Google Scholar 

  21. —:A new class of function spaces. Proc.Conf. "Constructive Function Theory", Kiew 1983.

    Google Scholar 

  22. —:Compactness in translation invariant Banach spaces of distributions and compact multipliers, J.Math.Anal. Appl.102, 289–327 (1984).

    Article  MATH  MathSciNet  Google Scholar 

  23. —:A characterization of minimal homogeneous Banach spaces. Proc.Amer.Math.Soc. 81, 55–61(1981).

    Article  MATH  MathSciNet  Google Scholar 

  24. —: Minimal Banach spaces and atomic decompositions. Publ. Math. Debrecen 33, 167–168 (1986) (An expanded version will appear in the same journal in 1987).

    Google Scholar 

  25. —: Atomic characterizations of modulation spaces. Proc. Conf. "Constructive Function Theory", Edmonton, July 1986, to appear.

    Google Scholar 

  26. —: The appropriate frame for harmonic analysis over locally compact abelian groups. Talk presented at the ICM 86, Berkeley.

    Google Scholar 

  27. M. FRAZIER, B. JAWERTH: Decomposition of Besov spaces. Indiana Univ.Math.J. 34, 777–799 (1985).

    Article  MATH  MathSciNet  Google Scholar 

  28. A. GROSSMANN, J. MORLET: Decomposition of Hardy functions into square integrable wavelets of constant shape. SIAM J.Math.Anal.15, 723–736 (1984).

    Article  MATH  MathSciNet  Google Scholar 

  29. A.GROSSMANN, J.MORLET: Decomposition of functions into wavelets of constant shape and related transforms. "Mathematics and Physics, Lect. on Recent Results", World Sci.Publ. Singapore.

    Google Scholar 

  30. A. GROSSMANN, J. MORLET, T. PAUL: Transforms associated to square integrable group representations I. J.Math.Phys. 26(10), 2473–2479 (1985).

    Article  MATH  MathSciNet  Google Scholar 

  31. A.GROSSMANN, T. PAUL: Wave functions on subgroups of the group of affine canonical transformations. In Proceedings "Resonances — Models and Phenomena", Bielefeld 1984, Lecture Notes in Physics 211, 128–138 (1984).

    Google Scholar 

  32. J. IGUSA: Theta Functions. Grundl.math.Wiss. Bd.194, Springer Berlin-Heidelberg-New York, 1972.

    Book  Google Scholar 

  33. S.JANSON, J.PEETRE, R.ROCHBERG: Hankel forms and the Fock space. Uppsala Univ.Dept.Math. Rep. 1986/6.

    Google Scholar 

  34. A.J. JANSSEN: Gabor representation of generalized functions. J.Math. Anal. Appl. 83, 377–394 (1981).

    Article  MATH  MathSciNet  Google Scholar 

  35. S. LANG: SL2 (ℝ), Springer, New York-Berlin-Heidelberg (1985).

    Google Scholar 

  36. D.H. LUECKING: Representations and duality in weighted spaces of analytic functions. Ind.Univ.Math.J. 34, 319–336(1985).

    Article  MATH  MathSciNet  Google Scholar 

  37. YMEYER: De la recherche petrolière á la géometrie des espaces de Banach en passant par les paraproduits. Sem.Equ.Der.Part. 1985/86, Ecole Polytechn. Paris.

    Google Scholar 

  38. Y.MEYER: Principe d’incertitude, bases hilbertiennes et algèbres d’opérateurs. Séminaire Bourbaki, 38ème année, 1985/86 no 662.

    Google Scholar 

  39. A.PAPOULIS: Signal analysis. McGraw-Hill Book Comp.. 1977.

    Google Scholar 

  40. J.PEETRE: New Thoughts on Besov Spaces. Duke Univ.Math.Ser. 1, Durham, 1976.

    Google Scholar 

  41. J.PEETRE: Paracommutators and minimal spaces, Proc.Conf. "Operators and Function Theory",S.C.Powers ed., NATO ASI Series.,Reidel (1985).

    Google Scholar 

  42. H.REITER: Classical Harmonic Analysis and Locally Compact Groups. Oxford Univ.Press, (1968).

    Google Scholar 

  43. F. RICCI, M. TAIBLESON: Boundary values of harmonic functions in mixed norm spaces and their atomic structure. Ann. Scuola Norm.Sup. Pisa, Ser. IV, X 1–54 (1983).

    MathSciNet  Google Scholar 

  44. R.ROCHBERG: Decomposition theorems for Bergman spaces and their applications. In "Operators and Function Theory". S.C.Powers ed. NATO ASI Series. Reidel (1985).

    Google Scholar 

  45. W. SCHEMPP: Radar reception and nilpotent harmonic analysis I–IV. C.R. Math./ Math.Reports, Acad.Sci Canada 4, 43–48, 139–144, 219–224, 287–292 (1982).

    MATH  MathSciNet  Google Scholar 

  46. W. SCHEMPP: Radar ambiguity function, the Heisenberg group, and holomorphic theta series, Proc.Amer.Math.Soc. 92, 103–110(1984).

    Article  MATH  MathSciNet  Google Scholar 

  47. W. SCHEMPP: Harmonic analysis on the Heisenberg group with applications, Pitman, Boston, Mass.(1986).

    MATH  Google Scholar 

  48. M. TAYLOR, Noncommutative Harmonic Analysis. Math. Surveys and Monographs Nr.22. Amer.Math.Soc., Providence (1986).

    MATH  Google Scholar 

  49. H. TRIEBEL: Spaces of Besov-Hardy-Sobolev Type. Teubner Texte zur Mathematik. Teubner,Leipzig (1978).

    Google Scholar 

  50. H. TRIEBEL: Theory of Function Spaces. Akad. Verlagsges., Leipzig (1983).

    Book  Google Scholar 

  51. H. TRIEBEL: Modulation spaces on the Euclidean n-space, Zeitschr.für Analysis und ihre.Anwendungen 2, 443–457 (1983).

    MATH  MathSciNet  Google Scholar 

  52. H.TRIEBEL: Characterizations of Besov-Hardy-Sobolev-spaces. A unified approach. Preprint(1986).

    Google Scholar 

  53. G. WARNER: Harmonic Analysis on Semisimple Lie Groups I, II. Springer Berlin-Heidelberg-New York.1972.

    Book  Google Scholar 

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Michael Cwikel Jaak Peetre Yoram Sagher Hans Wallin

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Feichtinger, H.G., Gröchenig, K. (1988). A unified approach to atomic decompositions via integrable group representations. In: Cwikel, M., Peetre, J., Sagher, Y., Wallin, H. (eds) Function Spaces and Applications. Lecture Notes in Mathematics, vol 1302. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078863

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  • DOI: https://doi.org/10.1007/BFb0078863

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