Pseudodifferential operators on ultra-modulation spaces

Journal of Functional Analysis

Volumn 208, Issue 1, 2004, Pages 194-228

  Pilipovic S ^a   Teofanov, N ^a  

^a UNIVERSITY OF NOVI SAD   (Serbia)

Author keywords

Gabor frames; Modulations spaces; Pseudodifferential operators; Wilson bases

Indexed keywords

EID: 1442355395     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfa.2003.09.012     Document Type: Article

References (40)

1. P. Boggiatto, E. Buzano, L. Rodino, Global Hypoellipticity and Spectral Theory, Akademie Verlag GmbH, Berlin, 1996.
2. P. Boggiatto, E. Cordero, K. Gröchenig, Generalized anti-Wick operators with symbols in distributional Sobolev spaces, Integral Equations Operator Theory, to appear.
3. L. Boutet De Monvel, P. Kree, Pseudodifferential operators and Gevrey classes, Ann. Inst. Fourier 17 (1967) 295-323.
4. M. Cappiello, Pseudodifferential parametrices of infinite order for SG-hyperbolic problems, Rend. Sem. Mat. Univ. Politec. Torino 61 (2003).
5. O. Christensen, An Introduction to Frames and Riesz Bases, Birkhäuser, Boston Inc., Boston, MA, 2003.
6. E. Cordero, K. Gröchenig, Time-frequency analysis of localization operators, J. Funct. Anal. 205 (2003) 107-131.
7. W. Czaja, Z. Rzeszotnik, Pseudodifferential operators and Gabor frames: spectral asymptotics, Math. Nachr. 233-234 (2002) 77-88.
8. I. Daubechies, S. Jaffard, J. Journé, A simple Wilson orthonormal basis with exponential decay, SIAM J. Math. Anal. 22 (1991) 554-572.
9. H.G. Feichtinger, Modulation spaces on locally compact Abelian groups, Technical Report, Vienna, 1983.
10. R. Ramakrishnan, S. Thangavelu (Eds.), Proceedings of the International Conference on Wavelets and their Applications Chennai, January 2002, Allied Publishers, New Delhi, 2003.
11. H.G. Feichtinger, K. Gröchenig, Gabor wavelets and the Heisenberg group: Gabor expansion and short time Fourier transform from the group theoretical point of view, in: C.H. Chui (Ed.), Wavelets - A Tutorial in Theory and Applications, Academic Press, Boston, 1992.
12. H.G. Feichtinger, K. Gröchenig, Gabor frames and time-frequency analysis of distributions, J. Funct. Anal. 146 (1997) 464-495.
13. H.G. Feichtinger, K. Gröchenig, D. Walnut, Wilson bases and modulation spaces, Math. Nachr. 155 (1992) 7-17.
14. H.G. Feichtinger, T. Strohmer, Gabor Analysis and Algorithms: Theory and Applications, Birkhäuser, Boston Inc., Boston, MA, 1998.
15. H.G. Feichtinger, T. Strohmer, Advances in Gabor Analysis, Birkhäuser, Boston Inc., Boston, MA, 2003.
16. I.M. Gelfand, G.E. Shilov, Generalized Functions II, III, Academic Press, New York, London, 1967.
17. K. Gröchenig, Foundations of Time-Frequency Analysis, Birkhäuser, Boston, Basel, Berlin, 2001.
18. K. Gröchenig, C. Heil, Modulation spaces and pseudodifferential operators, Integral Equations Operator Theory 34 (1999) 439-457.
19. S. Hashimoto, T. Matsuzawa, Y. Morimoto, Opérateurs pseudodifférentiels et classes de Gevrey, Comm. Partial Differential Equations 8 (12) (1983) 1277-1289.
20. C. Heil, Integral operators, pseudodifferential operators, and Gabor frames, in: H.G. Feichtinger, T. Strohmer (Eds.), Advances in Gabor Analysis, Birkhäuser, Boston Inc., Boston, MA, 2003.
21. H. Komatsu, Ultradistributions I, structure theorems and a characterization, J. Fac. Sci. Univ. Tokyo Sect. IA 20 (1973) 25-105.
22. D. Labate, Time-frequency analysis of pseudodifferential operators, Monats. f. Math. 133 (2001) 143-156.
23. E. Magus, O. Tricomi, Higher Transcendental Functions, McGraw-Hill, New York, 1953.
24. T. Matsuzawa, Gevrey hypoellipticity of a class of pseudodifferential operators, Tohoku Math. J. 39 (1987) 447-464.
25. T. Matsuzawa, Hypoellipticity in ultradistribution spaces, J. Fac. Sci. Univ. Tokyo Sect. IA 34 (1987) 779-790.
26. S. Pilipović, Tempered ultradistributions, Boll. Un. Mat. Ital. 7 (1988) 235-251.
27. S. Pilipović, N. Teofanov, Wilson bases and ultramodulation spaces, Math. Nach. 242 (2002) 179-196.
28. S. Pilipović, N. Teofanov, On a class of pseudodifferential operators, Proceedings of the 10th Congress Yu. Math., Belgrade, 2001, pp. 267-270.
29. R. Rochberg, K. Tachizawa, Pseudodifferential operators, Gabor frames, and local trigonometric bases, in: H.G. Feichtinger, T. Strohmer (Eds.), Gabor Analysis and Algorithms: Theory and Applications, Birkhäuser, Boston Inc., Boston, MA, 1998.
30. L. Rodino, Linear Partial Differential Operators in Gevrey Classes, World Scientific, Singapore, 1993.
31. M.A. Shubin, Pseudodifferential Operators and Spectral Theory, Springer, Heidelberg, 2001.
32. K. Tachizawa, The boundedness of pseudodifferential operators on modulation spaces, Math. Nachr. 168 (1994) 263-277.
33. K. Tachizawa, The pseudodifferential operators and Wilson bases, J. Math. Pure Appl. 75 (1996) 509-529.
34. J. Toft, Continuity properties for modulation spaces, with applications to pseudo-differential calculus, I, J. Funct. Anal., to appear.
35. J. Toft, Modulation spaces of non standard type and pseudodifferential operators, Research Report Blekinge Institute of Technology, Karlskrona 2003:01, 2003, pp. 1-35.
36. F. Treves, Introduction to Pseudodifferential Operators and Fourier Integral Operators, Vol. I, Plenum Press, New York, London, 1982.
37. L.R. Volevic, Pseudodifferential operators with holomorphic symbols and Gevrey classes, Trans. Moscov Math. Soc. 24 (1974) 43-72.
38. A. Weinstein, W. Stenger, Methods of Intermediate Problems for Eigenvalues, Academic Press, New York, 1972.
39. M.W. Wong, Weyl Transforms, Springer, New York, 1998.
40. L. Zanghirati, Pseudodifferential operators of infinite order and Gevrey classes, Ann. Univ. Ferrara - Sez. VII - Sc. Mat. 31 (1985) 197-219.