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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Spectral analysis of finite convolution operators
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by Richard Frankfurt PDF
Trans. Amer. Math. Soc. 214 (1975), 279-301 Request permission

Abstract:

In this paper the similarity problem for operators of the form $( \ast )\;T:f(x) \to \smallint _0^xk(x - t)f(t)dt$ on ${L^2}(0,1)$ is studied. Let $K(z) = \smallint _0^1\;k(t){e^{itz}}dt$. A function $C(z)$ is called a symbol for T if $C(z)$ can be written in the form $C(z) = K(z) + {e^{iz}}G(z)$, where $G(z)$ is a function bounded and analytic in a half plane $y > \delta$, for some real number $\delta$. Under suitable restrictions, it is shown that two operators of the form $( \ast )$ will be similar if they possess symbols which are asymptotically close together as $z \to \infty$ in some half plane $y > \delta$.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 214 (1975), 279-301
  • MSC: Primary 47G05; Secondary 44A35
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0397481-9
  • MathSciNet review: 0397481