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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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The behavior of the heat operator on weighted Sobolev spaces
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by G. N. Hile and C. P. Mawata PDF
Trans. Amer. Math. Soc. 350 (1998), 1407-1428 Request permission

Abstract:

Denoting by ${\mathcal {H}}$ the heat operator in $R^{n+1}$, we investigate its properties as a bounded operator from one weighted Sobolev space to another. Our main result gives conditions on the weights under which ${\mathcal {H}}$ is an injection, a surjection, or an isomorphism. We also describe the range and kernel of ${\mathcal {H}}$ in all the cases. Our results are analogous to those obtained by R. C. McOwen for the Laplace operator in $R^{n}$.
References
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Additional Information
  • G. N. Hile
  • Affiliation: University of Hawaii, Manoa, 2565 The Mall, Honolulu, Hawaii 96822
  • Email: hile@math.hawaii.edu
  • C. P. Mawata
  • Affiliation: University of Tennessee, Chattanooga, 615 McCallie Avenue, Chattanooga, Tennessee 37403
  • Email: cmawata@cecasun.utc.edu
  • Received by editor(s): April 12, 1996
  • © Copyright 1998 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 1407-1428
  • MSC (1991): Primary 35B45; Secondary 35A05, 35J60
  • DOI: https://doi.org/10.1090/S0002-9947-98-02140-0
  • MathSciNet review: 1467466