Gabor pairs, and a discrete approach to wave-front sets

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• 作者：Karoline Johansson (1)
  Stevan Pilipovi? (2)
  Nenad Teofanov (2)
  Joachim Toft (1)
  
• 关键词：Wave ; front ; Fourier ; Lebesgue ; Modulation ; Micro ; local ; 35A18 ; 35S30 ; 42B05 ; 35H10
• 刊名：Monatshefte f眉r Mathematik
• 出版年：2012
• 出版时间：May 2012
• 年：2012
• 卷：166
• 期：2
• 页码：181-199
• 全文大小：230KB
• 参考文献：1. Feichtinger, H.G.: Modulation spaces on locally compact abelian groups. Technical report. University of Vienna, Vienna (1983); also In: Krishna, M., Radha, R., Thangavelu, S.: (eds.) Wavelets and Their Applications, pp. 99-40. Allied Publishers Private Limited, New Delhi, Mumbai, Kolkata, Chennai, Hagpur, Ahmadabad, Bangalore, Hyderabad, Lucknow (2003)
  2. Feichtinger H.G., Gr?chenig K.H.: Banach spaces related to integrable group representations and their atomic decompositions, I. J. Funct. Anal. 86, 307-40 (1989) CrossRef
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  6. Feichtinger, H.G., Strohmer, T. (eds): Advances in Gabor Analysis. Birkh?user, Basel (2003)
  7. Gr?chenig K.: Foundations of Time-Frequency Analysis. Birkh?user, Boston (2001)
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  12. Pilipovi?, S., Teofanov, N., Toft, J.: Micro-local analysis in Fourier–Lebesgue and modulation spaces, Part I. J. Fourier Anal. Appl. (2011) (in press)
  13. Pilipovi? S., Teofanov N., Toft J.: Micro-local analysis in Fourier–Lebesgue and modulation spaces. Part II. J. Pseudodiffer. Oper. Appl. 1(3), 341-76 (2010) CrossRef
  14. Ruzhansky M., Turunen V.: Pseudo-Differential Operators and Symmetries: Background Analysis and Advanced Topics. Birkh?user, Boston (2010)
  15. Ruzhansky M., Turunen V.: Quantization of pseudo-differential operators on the torus. J. Fourier Anal. Appl. 16(6), 943-82 (2010) CrossRef
  16. Toft J.: Multiplication properties in pseudo-differential calculus with small regularity on the symbols. J. Pseudodiffer. Oper. Appl. 1, 101-38 (2010) CrossRef
  
• 作者单位：Karoline Johansson (1)
  Stevan Pilipovi? (2)
  Nenad Teofanov (2)
  Joachim Toft (1)
  
  1. Department of Computer Science, Physics and Mathematics, Linn?us University, V?xj?, Sweden
  2. Department of Mathematics and Informatics, University of Novi Sad, Novi Sad, Serbia
  
• ISSN：1436-5081

文摘

We introduce admissible lattices and Gabor pairs to define discrete versions of wave-front sets with respect to Fourier–Lebesgue and modulation spaces. We prove that these wave-front sets agree with each other and with corresponding wave-front sets of “continuous type- This implies that the coefficients of a Gabor frame expansion of f are parameter dependent, and describe the wave-front set of f.