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.References
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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