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Original Articles

Remarks on mapping properties for the Bargmann transform on modulation spaces

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Pages 359-366 | Received 25 Feb 2010, Accepted 09 Apr 2010, Published online: 17 May 2011

References

  • Bargmann , V. 1961 . On a Hilbert space of analytic functions and an associated integral transform . Comm. Pure Appl. Math. , 14 : 187 – 214 .
  • Bargmann , V. 1967 . On a Hilbert space of analytic functions and an associated integral transform. Part II. A family of related function spaces. Application to distribution theory . Comm. Pure Appl. Math. , 20 : 1 – 101 .
  • Boggiatto , P. , Cordero , E. and Gröchenig , K. 2004 . Anti-Wick generalized operators with symbol in distributional Sobolev spaces . Integr. Equ. Oper. Theory , 48 : 427 – 442 .
  • Feichtinger , H. G. 1983 . “ Modulation spaces on locally compact abelian groups ” . Vienna : University of Vienna . Tech. Rep. (also in M. Krishna, R. Radha, and S. Thangavelu, eds., Wavelets and their Applications, Allied Publishers, New Dehli, 2003, pp. 99–140)
  • Feichtinger , H. G. and Gröchenig , K. H. 1989 . Banach spaces related to integrable group representations and their atomic decompositions, I . J. Funct. Anal. , 86 : 307 – 340 .
  • Feichtinger , H. G. and Gröchenig , K. H. 1989 . Banach spaces related to integrable group representations and their atomic decompositions, II . Monatsh. Math. , 108 : 129 – 148 .
  • Feichtinger , H. G. , Gröchenig , K. H. and Walnut , D. 1992 . Wilson bases and modulation spaces . Math. Nachr. , 155 : 7 – 17 .
  • Gröchenig , K. 1991 . Describing functions: Atomic decompositions versus frames . Monatsh. Math. , 112 : 1 – 42 .
  • Gröchenig , K. 2001 . Foundations of Time-Frequency Analysis , Boston : Birkhäuser .
  • Gröchenig , K. and Toft , J. Isomorphism properties of Toeplitz operators and pseudo-differential operators between modulation spaces . preprint (2009). Available at arXiv:arXiv:0905.4954
  • Gröchenig , K. and Walnut , D. 1992 . A Riesz basis for Bargmann-Fock space related to sampling and interpolation . Ark. Mat. , 30 : 283 – 295 .
  • Hörmander , L. 1983, 1985 . The Analysis of Linear Partial Differential Operators , Vol. I–III , Berlin, Heidelberg : Springer-Verlag .
  • Janson , S. , Petree , J. and Rochberg , R. 1987 . Hankel forms and the Fock space . Rev. Mat. Iberoamericana , 3 : 61 – 138 .
  • Reed , M. and Simon , B. 1979 . Methods of Modern Mathematical Physics , London : Academic Press .
  • Signahl , M. and Toft , J. “ Mapping properties for the Bargmann transform on modulation spaces ” . preprint (2010). Available at arXiv:1002.3061
  • Toft , J. 2004 . Continuity properties for modulation spaces with applications to pseudo-differential calculus, II . Ann. Global Anal. Geom. , 26 : 73 – 106 .
  • Toft , J. 2004 . Minizization under entropy conditions, with applications in lower bound problems . J. Math. Phys. , 45 : 3216 – 3227 .
  • Toft , J. 2007 . “ Continuity and Schatten properties for pseudo-differential operators on modulation spaces ” . In Modern Trends in Pseudo-Differential Operators, Operator Theory: Advances and Applications , Edited by: Toft , J. , Wong , M. W. and Zhu , H. 173 – 206 . Basel : Birkhäuser Verlag .

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