Some 2-norm-based deviation estimations associated with the Fourier partial sum
Abstract
The analysis theory associated with linear 2-normed spaces has interested some mathematicians in recent decades. In contrast to the classical norm, 2-norm is an area-like metric instead of a length metric of vectors. This paper addresses the estimation of area-like deviation under 2-norm using Fourier partial sums. In the Hilbert space setting, we present an estimation of the area-like deviation and apply it to the Sobolev class, principle shift-invariant subspaces of [Formula: see text] and the Paley–Wiener space. We introduce the concepts of generalized Sobolev class and generalized Hölder class which are more general than the classical Sobolev class and classical Hölder class, and estimate the area-like deviation associated with them.
Fields of Study & Subjects
Advanced Harmonic Analysis Research
Approximation Theory and Sequence Spaces
Mathematical Analysis and Transform Methods
Publication details
- Journal / source
- International Journal of Wavelets Multiresolution and Information Processing
- Publisher
- World Scientific Pub Co Pte Ltd
- Volume
- 24
- Issue
- 02
- Publication date
- 22 January 2026
- Language
- EN