Nonlinear interpolation and norm minimization

A. A. Zhensykbaev

Al-Farabi Kazakh National University

Abstract: We prove that the set of convolution-type functions in $\mathbb R_d$ that satisfy the interpolation conditions contains a unique function whose convolution element has the minimum $L_p$-norm. The extremal function is determined by solving a nonlinear interpolation problem. The results are applied to an operator recovery problem.

Received: 16.05.1994

 English version: Mathematical Notes, 1995, 58:4, 1033–1041

Bibliographic databases:

• 
• 
•