Kyungpook Mathematical Journal

  • 제54권1호
  • /
  • Pages.43-63
  • /
  • 2014
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
권호 표지
DOI QR코드

DOI QR Code

Fourier Cosine and Sine Transformable Boehmians

  • 투고 : 2011.05.16
  • 심사 : 2013.11.13
  • 발행 : 2014.03.23
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

The range spaces of Fourier cosine and sine transforms on $L^1$([0, ${\infty}$)) are characterized. Using Fourier cosine and sine type convolutions, Fourier cosine and sine transformable Boehmian spaces have been constructed, which properly contain $L^1$([0, ${\infty}$)). The Fourier cosine and sine transforms are extended to these Boehmian spaces consistently and their properties are established.

키워드

참고문헌

  1. T. K. Boehme, The support of Mikusinski operators, Trans. Amer. Math. Soc., 176(1973), 319-334.
  2. V. A. Kakichev, N. X Thao and V. K. Tuan, On the generalized convolutions for Fourier cosine and sine transforms, East-West J. Math., 1(1998), 85-90.
  3. Y. Katznelson, An introduction to harmonic analysis, Dover, (1976).
  4. P. J. Miana, Convolutions, Fourier trigonometric transforms and applications, Integral Transform. Spec. Funct., 16(2005), 583-585. https://doi.org/10.1080/10652460410001672951
  5. J. Mikusinski and P. Mikusinski, Quotients de suites et leurs applications dans l'analyse fonctionnelle, C.R. Acad. Sc. Paris, 293, Serie I (1981), 463-464.
  6. P. Mikusinski, Convergence of Boehmians, Japan. J. Math. (N.S.), 9(1983), 159-179. https://doi.org/10.4099/math1924.9.159
  7. P. Mikusinski, The Fourier transform of tempered Boehmians, Fourier Analysis, Lecture Notes in Pure and Appl. Math., Marcel Dekker, New York, (1994), 303-309.
  8. P. Mikusinski, Tempered Boehmians and ultra distributions, Proc. Amer. Math. Soc., 123(1995), 813-817. https://doi.org/10.1090/S0002-9939-1995-1223517-7
  9. P. Mikusinski, On fiexibility of Boehmians, Integral transform. Spec. Funct., 4(1996), 141-146. https://doi.org/10.1080/10652469608819101
  10. W. Rudin, Real and complex analysis, McGraw-Hill Book Company, New York, 1987.
  11. I. N. Sneddon, The use of integral transforms, McGraw-Hill International Editions, New York, 1972.
  12. E. C. Titchmarsh, Introduction to the theory of Fourier integrals, Oxford University Press, 1948.