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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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Product integral techniques for abstract hyperbolic partial differential equations
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by J. W. Spellmann PDF
Trans. Amer. Math. Soc. 209 (1975), 353-365 Request permission

Abstract:

Explicit and implicit product integral techniques are used to represent a solution $U$ to the abstract system: ${U_{12}}(x,y) = AU(x,y);U(x,0) = p = U(0,y)$. The coefficient $A$ is a closed linear transformation defined on a dense subspace $D(A)$ of the Banach space $X$ and the point $p$ in $D(A)$ satisfies the condition that $||{A^i}p|| < {S^i}{(i!)^{3/2}}$ for all integers $i \geqslant 0$ and some $S > 0$. The implicit technique is developed under the additional assumption that $A$ generates a strongly continuous semigroup of bounded linear transformations on $X$. Both methods provide representations for the ${J_0}$ Bessel function.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 209 (1975), 353-365
  • MSC: Primary 47D05; Secondary 35R20
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0377590-0
  • MathSciNet review: 0377590