Fourier multipliers of classical modulation spaces

Applied and Computational Harmonic Analysis

Volumn 21, Issue 3, 2006, Pages 349-359

  Feichtinger, Hans G ^a   Narimani, Ghassem ^b  

^a UNIVERSITY OF VIENNA   (Austria)

^b UNIVERSITY OF TABRIZ   (Iran)

Author keywords

Fourier multipliers; Modulation spaces; Pointwise multipliers; Wiener amalgam spaces

Indexed keywords

CONVOLUTION; FOURIER TRANSFORMS; FREQUENCY MULTIPLYING CIRCUITS; MATHEMATICAL OPERATORS;

FOURIER MULTIPLIERS; MODULATION SPACES; POINTWISE MULTIPLIERS; WIENER AMALGAM SPACES;

STATE SPACE METHODS;

EID: 33646557719     PISSN: 10635203     EISSN: 1096603X     Source Type: Journal    
DOI: 10.1016/j.acha.2006.04.010     Document Type: Article

References (25)

1. Bènyi A., Grafakos L., Gröchenig K., and Okoudjou K.A. A class of Fourier multipliers for modulation spaces. Appl. Comput. Harmon. Anal. 19 1 (2005) 131-139
2. Cordero E., and Gröchenig K. Time-frequency analysis of localization operators. J. Funct. Anal. 205 1 (2003) 107-131
3. Feichtinger H.G. Multipliers of Banach space of functions on groups. Math. Z. 152 (1976) 47-58
4. Feichtinger H.G. Un espace de Banach de distributions témperées sur les groups localement compactes abéliens. C. R. Acad. Sci. Paris Sér. A-B 290 17 (1980) A791-A794
5. Feichtinger H.G. A characterization of minimal homogeneous Banach spaces. Proc. Amer. Math. Soc. 81 (1981) 451-471
6. Feichtinger H.G. On a new Segal algebra. Monatsh. Math. 92 4 (1981) 269-289
7. Feichtinger H.G. Banach spaces of distributions of Wiener type and interpolation. In: Butzer P., Nagy B.Sz., and Görlich E. (Eds). Proc. Conf. Oberwolfach, Functional Analysis and Approximation. Oberwolfach, August 1980. Internat. Ser. Numer. Math. vol. 60 (1981), Birkhäuser, Basel 153-165
8. Feichtinger H.G. Banach convolution algebras of Wiener type. Functions, Series, Operators, vols. I, II. Budapest, 1980 (1983), North-Holland, Amsterdam 509-524
9. Feichtinger H.G. Generalized amalgams, with applications to Fourier transform. Canad. J. Math. 42 (1990) 395-409
10. H.G. Feichtinger, Modulation spaces on locally compact Abelian groups, in: R. Ramakrishnan, S. Thangavelu (Eds.), Proc. Int. Conf. Wavelets and Applications, Chennai, India, Allied Publishers, New Delhi, 2003, pp. 99-140. Reprint of 1983 technical report
11. Feichtinger H.G. Modulation spaces: Looking back and ahead. Sampl. Theory Signal Image Process. 5 2 (2006) 109-140
12. Feichtinger H.G., and Gröbner P. Banach spaces of distributions defined by decomposition methods I. Math. Nachr. 123 (1985) 97-120
13. Grafakos L. Classical and Modern Fourier Analysis (2004), Prentice-Hall, Upper Saddle River, NJ
14. Gröchenig K. Foundations of Time-Frequency Analysis (2001), Birkhäuser, Boston
15. C. Heil, An introduction to weighted Wiener amalgams, in: R. Ramakrishnan, S. Thangavelu (Eds.), Proc. Int. Conf. Wavelets and Applications, Chennai, India, Allied Publishers, New Delhi, 2003, pp. 183-216
16. q. J. London Math. Soc. (2) 10 (1975) 295-305
17. p spaces. Acta Math. 104 (1960) 93-140
18. Larsen R. An Introduction to the Theory of Multipliers (1979), Springer-Verlag, New York
19. Losert V. A characterization of minimal strongly character invariant Segal algebra. Ann. Inst. Fourier (Grenoble) 30 3 (1980) 129-139
20. Losert V. Segal algebras with functorial properties. Monatsh. Math. 96 3 (1983) 209-237
21. Poguntke D. Gewisse Segalsche Algebren auf lokalkompakten Gruppen. Arch. Math. 33 (1980) 454-460
22. Stein E.M. Singular Integrals and Differentiability Properties of Functions (1970), Princeton Univ. Press, Princeton, NJ
23. Toft J. Continuity properties for modulation spaces, with applications to pseudodifferential operators I. J. Funct. Anal. 207 2 (2004) 399-429
24. Toft J. Continuity properties for modulation spaces, with applications to pseudodifferential operators II. Ann. Global Anal. Geom. 16 1 (2004) 73-106
25. Triebel H. Theory of Function Spaces (1983), Birkhäuser, Boston