Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A sampling theorem on homogeneous manifolds
HTML articles powered by AMS MathViewer

by Isaac Pesenson PDF
Trans. Amer. Math. Soc. 352 (2000), 4257-4269 Request permission

Abstract:

We consider a generalization of entire functions of spherical exponential type and Lagrangian splines on manifolds. An analog of the Paley-Wiener theorem is given. We also show that every spectral entire function on a manifold is uniquely determined by its values on some discrete sets of points.

The main result of the paper is a formula for reconstruction of spectral entire functions from their values on discrete sets using Lagrangian splines.

References
  • John J. Benedetto, Irregular sampling and frames, Wavelets, Wavelet Anal. Appl., vol. 2, Academic Press, Boston, MA, 1992, pp. 445–507. MR 1161260
  • Jeff Cheeger, Mikhail Gromov, and Michael Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, J. Differential Geometry 17 (1982), no. 1, 15–53. MR 658471
  • Pierre Gilles Lemarié, Base d’ondelettes sur les groupes de Lie stratifiés, Bull. Soc. Math. France 117 (1989), no. 2, 211–232 (French, with English summary). MR 1015808
  • Yu. Lyubarskiĭ and W. R. Madych, The recovery of irregularly sampled band limited functions via tempered splines, J. Funct. Anal. 125 (1994), no. 1, 201–222. MR 1297019, DOI 10.1006/jfan.1994.1122
  • I. Z. Pesenson, The Bernstein inequality in representations of Lie groups, Dokl. Akad. Nauk SSSR 313 (1990), no. 4, 803–806 (Russian); English transl., Soviet Math. Dokl. 42 (1991), no. 1, 87–90. MR 1080635
  • Isaac Pesenson, Sampling of Paley-Wiener functions on stratified groups, J. Fourier Anal. Appl. 4 (1998), no. 3, 271–281. MR 1650917, DOI 10.1007/BF02476027
  • John Roe, An index theorem on open manifolds. I, II, J. Differential Geom. 27 (1988), no. 1, 87–113, 115–136. MR 918459
  • I. J. Schoenberg, Cardinal spline interpolation, Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 12, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1973. MR 0420078
  • M. A. Shubin, Spectral theory of elliptic operators on noncompact manifolds, Astérisque 207 (1992), 5, 35–108. Méthodes semi-classiques, Vol. 1 (Nantes, 1991). MR 1205177
  • Robert S. Strichartz, Analysis of the Laplacian on the complete Riemannian manifold, J. Functional Analysis 52 (1983), no. 1, 48–79. MR 705991, DOI 10.1016/0022-1236(83)90090-3
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 43A85, 58G03, 41A15
  • Retrieve articles in all journals with MSC (2000): 43A85, 58G03, 41A15
Additional Information
  • Isaac Pesenson
  • Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
  • MR Author ID: 196903
  • Email: pesenson@math.temple.edu
  • Received by editor(s): June 17, 1997
  • Received by editor(s) in revised form: June 26, 1998
  • Published electronically: April 21, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 352 (2000), 4257-4269
  • MSC (2000): Primary 43A85, 58G03; Secondary 41A15
  • DOI: https://doi.org/10.1090/S0002-9947-00-02592-7
  • MathSciNet review: 1707201