Wiener amalgams and pointwise summability of Fourier transforms and Fourier series

Mathematical Proceedings of the Cambridge Philosophical Society

Volumn 140, Issue 3, 2006, Pages 509-536

  Feichtinger, Hans G ^a   Weisz, Ferenc ^b  

^a UNIVERSITY OF VIENNA   (Austria)

^b EÖTVÖS LORÁND UNIVERSITY   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33646352993     PISSN: 03050041     EISSN: 14698064     Source Type: Journal    
DOI: 10.1017/S0305004106009273     Document Type: Article

References (46)

1. G. ALEXITS. Konvergenzeprobleme der Orthogonalreihen (Akadémiai Kiadó 1960).
2. H. BERENS, Z. LI and Y. XU. On l-1 Riesz summability of the inverse Fourier integral. Indag. Math. 12 (2001), 41-53.
3. H. BEBENS and Y. XU. l-1 summability of multiple Fourier integrals and positivity. Math. Proc. Camb. Phil. Soc. 122 (1997), 149-172.
4. J. BERGH and J. LÖFSTRÖM. Interpolation Spaces, an Introduction (Springer, 1976).
5. J. BOKOR and F. SCHIPP. Approximate identification in Laguerre and Kautz bases. Automatica 34 (1998), 463-468.
6. P. L. BUTZER and R. J. NESSEL. Fourier Analysis and Approximation (Birkhäuser Verlag, 1971).
7. ptheory on product domains. Bull. Amer. Math. Soc. 12 (1985), 1-43.
8. K. M. DAVIS and Y.-C. CHANG. Lectures on Bochner-Riesz Means, volume 114 of London Mathematical Society Lecture Note Series (Cambridge University Press, 1987).
9. d) and norm summability of Fourier series and Fourier transforms. To appear in Monatsh. Math. (2006).
10. H. G. FEICHTINGER and G. ZIMMERMANN. A Banach space of test functions for Gabor analysis. In H. G. Feichtinger and T. Strohmer, editors, Gabor Analysis and Algorithms. Theory and Applications. Appl. Numer. Harmon. Anal. ch. 3 (1998), 123-170.
11. H. G. FEICHTINGER. On a new Segal algebra. Monatsh. Math. 92 (1981), 269-289.
12. H. G. FEICHTINGER. Minimal Banach spaces and atomic representations. Publ. Math. Debrecen 34 (1987), 231-240.
13. H. FEICHTINGER. An elementary approach to Wiener's third Tauberian theorem for the Euclidean n-space. In Symposia Math., volume XXIX of Analisa Armonica (Cortona, 1988) pp. 267-301.
14. L. FEJÉR. Untersuchungen über Fouriersche Reihen. Math. Ann. 58 (1904), 51-69.
15. J. GARCIA-CUERVA and M.-J. L. HERRERO. A theory of Hardy spaces associated to the Herz spaces. Proc. London Math. Soc. 69 (1994), 605-628.
16. G. GAT. On the divergence of the (C, 1) means of double Walsh-Fourier series. Proc. Amer. Math. Soc. 128 (2000), 1711-1720.
17. M. GIRARDI and L. WEIS. Operator-valued Fourier multiplier theorems on Besov spaces. Math. Nachr. 251 (2003), 34-51.
18. L. GRAFAKOS. Classical and Modern Fourier Analysis (Pearson Education, 2004).
19. K. GRÖOHENIG. An uncertainty principle related to the Poisson summation formula. Studia Math. 121 (1996), 87-104.
20. K. GRÖCHENIG. Foundations of Time-Frequency Analysis (Birkhäuser, 2001).
21. C. HEIL. An introduction to weighted Wiener amalgams. In M. Krishna, R. Radha and S. Thangavelu, editors, Wavelets and their Applications (Allied Publishers Private Limited, 2003) pp. 183-216.
22. C. HERZ. Lipschitz spaces and Bernstein's theorem on absolutely convergent Fourier transforms. J. Math. Mech. 18 (1968), 283-324.
23. H. LEBESGUE. Recherches sur la convergence des séries de Fourier. Math. Ann. 61 (1905), 251-280.
24. V. LOSERT. A characterization of the minimal strongly character invariant Segal algebra. Ann. Inst. Fourier (Grenoble) 30 (1980), 129-139.
25. p Spaces (World Scientific, 1995).
26. J. MAROINKIEWICZ and A. ZYGMUND. On the summability of double Fourier series. Fund. Math. 32 (1939), 122-132.
27. J. MARCINKIEWICZ. Sur une méhode remarquable de sommation des séries doubles de Fourier. Ann. Scuola Norm. Sup. Pisa 8 (1939), 149-160.
28. G. M. NATANSON and V. V. ZUK. Trigonometric Fourier Series and Approximation Theory (Izdat. Leningrad Unta, Leningrad, 1983). (In Russian.)
29. J. PEETRE. Applications de la théorie des espaces d'interpolation dans l'analyse harmonique. Ricerche Mat. 15 (1966), 1-37.
30. T. RUNST and W. SIOKEL. Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations (Walter de Gruyter, 1996).
31. ∞ system approximation algorithms generated by if summations. Automatica 33 (1997), 2019-2024.
32. ∞-norm. In Approximation Theory and Function Series, volume 5 (Bolyai Soc. Math. Studies, Budapest, 1996), 307-320.
33. E. M. STEIN and G. WEISS. Introduction to Fourier Analysis on Euclidean Spaces (Princeton University Press, 1971).
34. E. M. STEIN. On limits of sequences of operators. Ann. of Math. 74 (1961), 140-170.
35. E. M. STEIN. Harmonic Analysis: Real-variable Methods, Orthogonality and Oscillatory Integrals (Princeton University Press, 1993).
36. L. SZILI and P. VÉRTESI. On uniform convergence of sequences of certain linear operators. Acta Math. Hungar. 91 (2001), 159-186.
37. L. SZILI. On the summability of trigonometric interpolation processes. Acta Math. Hungar. 91 (2001), 131-158.
38. A. TORCHINSKY. Real-variable Methods in Harmonic Analysis (Academic Press, 1986).
39. H. TRIEBEL. Theory of Function Spaces II (Birkhäuser, 1992).
40. F. WEISZ. Cesàro summability of multi-dimensional trigonometric-Fourier series. J. Math. Anal. Appl. 204 (1996), 419-431.
41. F. WEISZ. θ-summation and Hardy spaces. J. Approx. Theory 107 (2000), 121-142.
42. F. WEISZ. Several dimensional θ-summability and Hardy spaces. Math. Nachr. 230 (2001), 159-180.
43. F. WEISZ. Summability of Multi-dimensional Fourier Series and Hardy Spaces. Mathematics and Its Applications (Kluwer Academic Publishers, 2002).
44. F. WEISZ. θ-summability of Fourier series. Acta Math. Hungar. 103 (2004), 139-176.
45. L. ZHIZHIASHVILI. Trigonometric Fourier Series and their Conjugates (Kluwer Academic Publishers, 1996).
46. A. ZYGMUND. Trigonometric Series (Cambridge Press, 2002) 3rd edition.