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Schatten p-class property of pseudodifferential operators with symbols in modulation spaces

  • Masaharu Kobayashi (a1) and Akihiko Miyachi (a2)

Abstract

It is proved that the pseudodifferential operators σt(X, D) belong to the Schatten p-class Cp , 0 < p ≤ 2, if the symbol σ(x,ω) is in certain modulation spaces on

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References

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[1] Arsu, G., On Schatten-von Neumann class properties of pseudodifferential operators: The Cordes-Kato method, J. Operator Theory 59 (2008), 81114.
[2] Dunford, N. and Schwartz, J. T., Linear Operators, II: Spectral Theory, John Wiley, New York, 1963.
[3] Feichtinger, H. G., “Modulation spaces on locally compact abelian groups” in Wavelets and Their Applications, Allied, New Delhi, 2003, 99140.
[4] Folland, G. B., Harmonic Analysis in Phase Space, Ann. of Math. Stud. 122, Princeton University Press, Princeton, 1989.
[5] Galperin, Y. and Samarah, S., Time-frequency analysis on modulation spaces Mm p,q,0 < p,q ≤ ∞, Appl. Comput. Harmon. Anal. 16 (2004), 118.
[6] Gröchenig, K., An uncertainty principle related to the Poisson summation formula, Studia Math. 121 (1996), 87104.
[7] Gröchenig, K., Foundations of Time-Frequency Analysis, Birkhäuser, Boston, 2001.
[8] Gröchenig, K., “A pedestrian’s approach to pseudodifferential operators” in Harmonic Analysis and Applications, Birkhäuser, Boston, 2006, 139169.
[9] Gröchenig, K. and Heil, C., Modulation spaces and pseudodifferential operators, Integral Equations Operator Theory 34 (1999), 439457.
[10] Gröchenig, K. and Heil, C., Counterexamples for boundedness of pseudodifferential operators, Osaka J. Math. 41 (2004), 681691.
[11] Heil, C., History and evolution of the density theorem for Gabor frames, J. Fourier Anal. Appl. 13 (2007), 113166.
[12] Heil, C., Ramanathan, J., and Topiwala, P., Singular values of compact pseudodiffer-ential operators, J. Funct. Anal. 150 (1997), 426452.
[13] Kobayashi, M., Modulation spaces Mp,q for 0 < p,q ≤ ∞, J. Funct. Spaces Appl. 4 (2006), 329341.
[14] Komatsu, H., Theory of Locally Convex Spaces, Lecture Notes, Department of Math., Univ. of Tokyo, Tokyo, 1974.
[15] McCarthy, C. A., Cp , Israel J. Math. 5 (1967), 249271.
[16] Meise, R. and Vogt, D., Introduction to Functional Analysis, Oxf. Grad. Texts Math. 2, Oxford University Press, New York, 1997.
[17] Rauhut, H., Coorbit space theory for quasi-Banach spaces, Studia Math. 180 (2007), 237253.
[18] Rochberg, R. and Tachizawa, K., “Pseudodifferential operators, Gabor frames, and local trigonometric bases” in Gabor Analysis and Algorithms, Appl. Numer. Harmon. Anal., Birkhäuser, Boston, 1998, 171192.
[19] Rondeaux, C., Classes de Schatten d’opérateurs pseudo-différentiels, Ann. Sci. Ec. Norm. Supéer. (4) 17 (1984), 6781.
[20] Schatten, R., Norm Ideals of Completely Continuous Operators, Ergeb. Math. Grenz-geb. (3) 27, Springer, Berlin, 1960.
[21] Seip, K., Density theorems for sampling and interpolation in the Bargman-Fock space, I, J. Reine. Angew. Math. 429 (1992), 91106.
[22] Seip, K. and Wallstén, R., Density theorems for sampling and interpolation in the Bargman-Fock space, II, J. Reine. Angew. Math. 429 (1992), 107113.
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