Tohoku Mathematical Journal

Saturation of the approximation by spectral decompositions

Miho Tanigaki

Full-text: Open access


We shall give a saturation class for approximations by eigenfunction expansions of the Laplacian in an open domain in the Euclidean space.

Article information

Tohoku Math. J. (2), Volume 52, Number 3 (2000), 431-447.

First available in Project Euclid: 3 May 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35P10: Completeness of eigenfunctions, eigenfunction expansions
Secondary: 35P05: General topics in linear spectral theory 47F05: Partial differential operators [See also 35Pxx, 58Jxx] (should also be assigned at least one other classification number in section 47)


Tanigaki, Miho. Saturation of the approximation by spectral decompositions. Tohoku Math. J. (2) 52 (2000), no. 3, 431--447. doi:10.2748/tmj/1178207822.

Export citation


  • [1] S A. ALIMOV AND V A IL'IN, Conditions for the convergence of spectral expansions corresponding to selfadjoint extensions of elliptic operators II (selfadjoint extensions of Laplace's operator with arbitrary spectra), Differential Equations 7 (1971), 651-670
  • [2] H BATEMAN, Higher transcendental functions, Volume II, McGraw-Hill Book Company, Inc New York, 1953
  • [3] N DUNFORD AND J T SCHWARTZ, Linear operators, Part II (Spectral theory), Pure and Appl Math. VII, Interscience Publishers, New York, 1963
  • [4] H FUJITA, S -T KURODA AND S I, Functional Analysis (Japanese), Iwanami Shoten, Tokyo, 199
  • [5] S IGARI, Saturation of the approximation by eigenfunctionexpansions associated with the Laplace operator, Tohoku Math. J 22 (1970), 231-239
  • [6] E C TITCHMARSH, Eigenfunctionexpansions associated with second order differential equations, Part II, Oxford Univ Press, Oxford, 1958
  • [7] G N WATSON, A treatise on the theory of Bessel functions, Cambridge Univ Press, Cambridge, 194