Next Article in Journal
Numerical Computation of 2D Domain Integrals in Boundary Element Method by (α, β) Distance Transformation for Transient Heat Conduction Problems
Previous Article in Journal
On Some Properties for Cofiniteness of Submonoids and Ideals of an Affine Semigroup
Previous Article in Special Issue
Multiplication Operators on Weighted Zygmund Spaces of the First Cartan Domain
 
 
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Consistent Sampling Approximations in Abstract Hilbert Spaces

1
Department of Mathematical Sciences, KAIST, Daejeon 34141, Republic of Korea
2
Department of Mathematics and Big Data Science, Kumoh National Institute of Technology, Gumi 39177, Republic of Korea
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Axioms 2024, 13(7), 489; https://doi.org/10.3390/axioms13070489
Submission received: 21 May 2024 / Revised: 6 July 2024 / Accepted: 19 July 2024 / Published: 21 July 2024
(This article belongs to the Special Issue Recent Advances in Functional Analysis and Operator Theory)

Abstract

This paper considers generalized consistent sampling and reconstruction processes in an abstract separable Hilbert space. Using an operator-theoretical approach, quasi-consistent and consistent approximations with optimal properties, such as possessing the minimum norm or being closest to the original vector, are derived. The results are illustrated with several examples.
Keywords: consistent sampling; generalized sampling; oblique projection; frame consistent sampling; generalized sampling; oblique projection; frame

Share and Cite

MDPI and ACS Style

Kang, S.; Kwon, K.H.; Lee, D.G. Consistent Sampling Approximations in Abstract Hilbert Spaces. Axioms 2024, 13, 489. https://doi.org/10.3390/axioms13070489

AMA Style

Kang S, Kwon KH, Lee DG. Consistent Sampling Approximations in Abstract Hilbert Spaces. Axioms. 2024; 13(7):489. https://doi.org/10.3390/axioms13070489

Chicago/Turabian Style

Kang, Sinuk, Kil Hyun Kwon, and Dae Gwan Lee. 2024. "Consistent Sampling Approximations in Abstract Hilbert Spaces" Axioms 13, no. 7: 489. https://doi.org/10.3390/axioms13070489

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop