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Softcover ISBN:  9781470473457 
Product Code:  SURV/274 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470474515 
Product Code:  SURV/274.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9781470473457 
eBook ISBN:  9781470474515 
Product Code:  SURV/274.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 274; 2023; 491 ppMSC: Primary 65; 62; Secondary 78; 94; 86
The goal of this book is to introduce the reader to methodologies in recovery problems for objects, such as functions and signals, from partial or indirect information. The recovery of objects from a set of data demands key solvers of inverse and sampling problems. Until recently, connections between the mathematical areas of inverse problems and sampling were rather tenuous. However, advances in several areas of mathematical research have revealed deep common threads between them, which proves that there is a serious need for a unifying description of the underlying mathematical ideas and concepts. Freeden and Nashed present an integrated approach to resolution methodologies from the perspective of both these areas.
Researchers in sampling theory will benefit from learning about inverse problems and regularization methods, while specialists in inverse problems will gain a better understanding of the point of view of sampling concepts. This book requires some basic knowledge of functional analysis, Fourier theory, geometric number theory, constructive approximation, and special function theory. By avoiding extreme technicalities and elaborate proof techniques, it is an accessible resource for students and researchers not only from applied mathematics, but also from all branches of engineering and science.
ReadershipGraduate students and researchers interested in sampling theory and inverse problems.

Table of Contents

Introductory remarks

Constituents of the univariate antenna problem

Regularization tools

Functional and Fourier analytic auxiliaries

Regularization methodologies

Matricial methodologies of resolution

Compact operator methodologies of resolution

Example realizations light: Univariate differentiation

Reconstruction and regularization methods

Regularization examples

Regularization methodologies in geotechnology

Sampling tools

Lattice point and special function theoretic auxiliaries

Sampling methodologies

Sampling over continuously connected pointsets

Sampling over discretely given pointsets

Polyharmonic finite bandwidth sampling

Polyharmonic infinite bandwidth sampling

Polymetaharmonic finite bandwidth sampling

Polymetaharmonic infinite bandwidth sampling

Sampling examples

Sampling methodologies in technology

Concluding remarks

Recovery as interconnecting whole


Additional Material

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The goal of this book is to introduce the reader to methodologies in recovery problems for objects, such as functions and signals, from partial or indirect information. The recovery of objects from a set of data demands key solvers of inverse and sampling problems. Until recently, connections between the mathematical areas of inverse problems and sampling were rather tenuous. However, advances in several areas of mathematical research have revealed deep common threads between them, which proves that there is a serious need for a unifying description of the underlying mathematical ideas and concepts. Freeden and Nashed present an integrated approach to resolution methodologies from the perspective of both these areas.
Researchers in sampling theory will benefit from learning about inverse problems and regularization methods, while specialists in inverse problems will gain a better understanding of the point of view of sampling concepts. This book requires some basic knowledge of functional analysis, Fourier theory, geometric number theory, constructive approximation, and special function theory. By avoiding extreme technicalities and elaborate proof techniques, it is an accessible resource for students and researchers not only from applied mathematics, but also from all branches of engineering and science.
Graduate students and researchers interested in sampling theory and inverse problems.

Introductory remarks

Constituents of the univariate antenna problem

Regularization tools

Functional and Fourier analytic auxiliaries

Regularization methodologies

Matricial methodologies of resolution

Compact operator methodologies of resolution

Example realizations light: Univariate differentiation

Reconstruction and regularization methods

Regularization examples

Regularization methodologies in geotechnology

Sampling tools

Lattice point and special function theoretic auxiliaries

Sampling methodologies

Sampling over continuously connected pointsets

Sampling over discretely given pointsets

Polyharmonic finite bandwidth sampling

Polyharmonic infinite bandwidth sampling

Polymetaharmonic finite bandwidth sampling

Polymetaharmonic infinite bandwidth sampling

Sampling examples

Sampling methodologies in technology

Concluding remarks

Recovery as interconnecting whole