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Publication Cover
Applicable Analysis
An International Journal
Volume 40, 1991 - Issue 2-3
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Original Articles

Isometrical identities and inverse formulas in the one-dimensional heat equation

S. Saitoh Department of Mathematics, Faculty of Engineering, Gunma University, Kiryu, 376, Japan
Pages 139-149 | Received 13 Feb 1990, Published online: 10 May 2007

References

  • Aronszajn , N. 1950 . Theory of reproducing kernels . Trans. Amer. Math. Soc , 68 : 337 – 401 .
  • Folland , G.B. 1976 . Introduction to Partial Differential Equations , Princeton Univ. Press .
  • Gradshteyn , I.S. and Ryzhik , I.M . 1980 . Table of Integrals, Series and Prod¬ucts , Academic Press .
  • Hawley , N.S. and Schiffer , M . 1965 . Half-order differentials on Riemann surfaces . Acta Math , 115 : 199 – 236 .
  • Hayashi , N. and Saitoh , S . 1990 . Analyticity and smoothing effect for the Schrodinger equations . Ann. Inst. Henri Poincare. Physique theoreque , 52 : 163 – 173 .
  • Saitoh , S. 1983 . Hilbert spaces induced by Hilbert space valued functions . Proc. Amer. Math. Soc , 89 : 74 – 78 .
  • Saitoh , S. 1983 . The Weierstrass transform and an isometry in the heat equation . Applicable Analysis , 16 : 1 – 6 .
  • Saitoh , S. 1988 . Theory of reproducing kernels and its applications . Pitman Research Notes in Math. Series , 1989

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