Localization operators and exponential weights for modulation spaces

Mediterranean Journal of Mathematics

Volumn 2, Issue 4, 2005, Pages 381-394

  Cordero, Elena ^a   Pilipović, Stevan ^b   Rodino, Luigi ^a   Teofanov, Nenad ^b  

^a UNIVERSITY OF TURIN   (Italy)

^b UNIVERSITY OF NOVI SAD   (Serbia)

Author keywords

Gelfand Shilov type spaces; Localization operator; Modulation space; Schatten class; Short time Fourier transform; Ultra distributions; Wigner distribution

Indexed keywords

EID: 29844438067     PISSN: 16605446     EISSN: 16605454     Source Type: Journal    
DOI: 10.1007/s00009-005-0052-8     Document Type: Article

References (26)

1. F.A. Berezin, Wick and anti-Wick symbols of operators, Mat. Sb. 86 (no. 128) (1971), 578-610.
2. P. Boggiatto, E. Cordero and K. Gröchenig, Generalized Anti-Wick operators with symbols in distributional Sobolev spaces, Integral Equations Operator Theory, 48 (2004), 427-442.
3. J. Chung, S.-Y. Chung and D. Kim, Characterization of the Gelfand-Shilov spaces via Fourier transforms, Proc. Amer. Math. Soc. 124 (no. 7) (1996), 2101-2108.
4. E. Cordero, Gelfand-Shilov window classes for weighted modulation spaces, preprint, 2005.
5. E. Cordero and K. Gröchenig, Symbolic calculus and Fredholm property for localization operators, preprint, 2005.
6. E. Cordero and K. Gröchenig, Time-frequency analysis of localization operators, J. Funct. Anal. 205 (no. 1) (2003), 107-131.
7. E. Cordero and L. Rodino, Wick calculus: a time-frequency approach, Osaka J. Math. 42 (no. 1) (2005) 43-63.
8. I. Daubechies, Time-frequency localization operators: a geometric phase space approach, IEEE Trans. Inform. Theory 34 (no. 4) (1988), 605-612.
9. H.G. Feichtinger, Modulation spaces on locally compact abelian groups, in: Wavelets and Their Applications, M. Krishna, R. Radha, S. Thangavelu eds., Allied Publishers, 99-140, 2003.
10. H.G. Feichtinger and K. Gröchenig, Banach spaces related to integrable group representations and their atomic decompositions I, J. Funct. Anal. 86 (no. 2) (1989), 307-340.
11. H.G. Feichtinger and K.H. Gröchenig, Banach spaces related to integrable group representations and their atomic decompositions II, Monatsh. Math. 108 (1989), 129-148.
12. G.B. Folland. Harmonic Analysis in Phase Space, Princeton Univ. Press, Princeton, NJ, 1989.
13. I.M. Gelfand and G.E. Shilov, Generalized Functions II, Academic Press, New York, 1968.
14. K. Gröchenig, Foundations of Time-Frequency Analysis, Birkhäuser, Boston, 2001.
15. K. Gröchenig and C. Heil, Modulation spaces and pseudodifferential operators, Integral Equations Operator Theory, 34 (no. 4) (1999), 439-457.
16. K. Gröchenig and G. Zimmermann, Hardy's theorem and the short-time Fourier transform of Schwartz functions, J. London Math. Soc. 63 (2001), 205-214.
17. K. Gröchenig and G. Zimmermann, Spaces of test functions via the STFT, J. Funct. Spaces Appl. 2 (no. 1) (2004), 25-53.
18. L. Hörmander, The Analysis of Linear Partial Differential Operators I, II, III, IV, Springer-Verlag, Berlin, 1983-1985.
19. A. Kamiński, D. Perišić and S. Pilipović, On various integral transformations of tempered ultradistributions, Demonstratio Math. 33 (no. 3) (2000), 641-655.
20. S. Pilipović, Tempered ultradistributions, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. 7 (no. 2) (1988), 235-251.
21. S. Pilipović and N. Teofanov, Pseudodifferential operators on ultra-modulation spaces, J. Funct. Anal. 208 (2004), 194-228.
22. L. Rodino, Linear Partial Differential Operators in Gevrey Spaces, World Scientific, Singapore, 1993.
23. C. Roumieu, Sur quelques extensions de la notion de distribution, Ann. Sci. École Norm Sup. 3 (no. 77) (1960), 41-121.
24. nd edition, 2001.
25. N. Teofanov, Ultradistributions and time-frequency analysis, in: Pseudo-differential Operators and Related Topics, Operator Theory: Advances and Applications, P. Boggiatto, L. Rodino, J. Toft, M.W. Wong eds., Birkhäuser, 164 (2006), 173-191.
26. N. Teofanov, Some remarks on ultra-modulation spaces, ESI preprint series 1685 (2005), 1-13.