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Time-invariant linear systems and a theorem of Titchmarsh

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Topics in Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 419))

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References

  1. Boas, R. P., Jr.: Entire functions.-Pure and Applied Mathematics V Academic Press Inc., Publishers, New York, 1954.

    MATH  Google Scholar 

  2. Boehme, T. K.: On approximate solutions to the convolution equation on the half-line.-Bull. Amer. Math. Soc. 69, 1963, pp. 847–849.

    Article  MathSciNet  MATH  Google Scholar 

  3. -"-The convolution integral.-SIAM Rev. 10, 1968, pp. 407–416.

    Article  MATH  Google Scholar 

  4. Cartwright, Mary L.: On functions which are regular and of finite order in an angle.-Proc. London Math. Soc. (2) 38, 1935, pp. 158–179.

    Article  MathSciNet  MATH  Google Scholar 

  5. Crum, M. M.: On the resultant of two functions.-Quart. J. Math. Oxford Ser. 12, 1941, pp. 108–111.

    Article  MathSciNet  MATH  Google Scholar 

  6. Fenyö, S.: Über den Zusammenhang zwischen den Mikusińskischen Operatoren und den Distributionen.-Math. Nachr. 19, 1958, pp. 161–164.

    Article  MathSciNet  MATH  Google Scholar 

  7. Foiaş, C.: Approximation des opérateurs de J. Mikusiński par des fonctions continues.-Studia Math. 21, 1961/1962, pp. 73–74.

    MathSciNet  MATH  Google Scholar 

  8. Kalisch, G. K.: A functional analysis proof of Titchmarsh's theorem on convolution.-J. Math. Anal. Appl. 5, 1962, pp. 176–183.

    Article  MathSciNet  MATH  Google Scholar 

  9. Mikusiński, J. [J. G.-Mikusiński]: Sur les fondements du calcul opératoire.-Studia Math. 11, 1950, pp. 41–70.

    MATH  Google Scholar 

  10. -"-A new proof of Titchmarsh's theorem on convolution.-Studia Math. 13, 1953, pp. 56–58.

    MathSciNet  MATH  Google Scholar 

  11. Operational calculus.-International Series of Monographs on Pure and Applied Mathematics 8. Pergamon Press, New York-London-Paris-Los Angeles / Państwowe Wydawnictwo Naukowe, Warszawa, 1959.

    Google Scholar 

  12. -"-An approximation theorem and its applications in operational calculus.-Studia Math. 27, 1966, pp. 141–145.

    MathSciNet  MATH  Google Scholar 

  13. -"-Convolution approximation and shift approximation.-Studia Math. 28, 1966/1967, pp. 1–8.

    MathSciNet  MATH  Google Scholar 

  14. Mikusiński, J., and Cz. Ryll-Nardzewski: Sur le produit de composition.-Studia Math. 12, 1951, pp. 51–57.

    MathSciNet  MATH  Google Scholar 

  15. Paley, R.E.A.C., and N. Wiener: Fourier transforms in the complex domain.-Colloquium Publications XIX. American Mathematical Society, New York, 1934.

    Google Scholar 

  16. Titchmarsh, E. C.: The zeros of certain integral functions.-Proc. London Math. Soc. (2) 25, 1926, pp. 283–302.

    Article  MathSciNet  MATH  Google Scholar 

  17. -"-Introduction to the theory of Fourier integrals.-The Clarendon Press, Oxford, 1st edition 1937 and 2nd edition 1948.

    Google Scholar 

  18. Weiss, B.: Titchmarsh's convolution theorem on groups.-Proc. Amer. Math. Soc. 19, 1968, pp. 75–79.

    MathSciNet  MATH  Google Scholar 

  19. Weston, J. D.: On the representation of operators by convolution integrals.-Pacific J. Math. 10, 1960, pp. 1453–1468.

    Article  MathSciNet  MATH  Google Scholar 

  20. -"-An algebraic theory of generalized functions.-Nieuw Arch. Wisk. (3) 18, 1970, pp. 211–249.

    MathSciNet  MATH  Google Scholar 

  21. Williamson, J. H.: The Wiener-Pitt phenomenon on the half-line.-Proc. Edinburgh Math. Soc. (2) 13, 1962, pp. 37–38.

    Article  MathSciNet  MATH  Google Scholar 

  22. Zadeh, L. A., and C. A. Desoer: Linear system theory: The state space approach.-Series in Systems Science. McGraw-Hill Book Company, Inc., New York etc., 1963.

    Google Scholar 

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Olli Lehto Ilppo Simo Louhivaara Rolf Nevanlinna

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© 1974 Springer-Verlag

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Weston, J.D. (1974). Time-invariant linear systems and a theorem of Titchmarsh. In: Lehto, O., Louhivaara, I.S., Nevanlinna, R. (eds) Topics in Analysis. Lecture Notes in Mathematics, vol 419. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064745

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  • DOI: https://doi.org/10.1007/BFb0064745

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  • Print ISBN: 978-3-540-06965-2

  • Online ISBN: 978-3-540-37907-2

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