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on1263743387 |
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OCoLC |
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20241006213017.0 |
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210813s2021 sz ob 001 0 eng d |
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|a YDX
|b eng
|e pn
|c YDX
|d GW5XE
|d EBLCP
|d OCLCO
|d OCLCF
|d OCLCQ
|d COM
|d OCLCO
|d OCLCQ
|d OCLCO
|d S9M
|d OCLCL
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| 019 |
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|a 1263868842
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| 020 |
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|a 9783030774974
|q (electronic bk.)
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| 020 |
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|a 303077497X
|q (electronic bk.)
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|z 3030774961
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| 020 |
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|z 9783030774967
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| 024 |
7 |
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|a 10.1007/978-3-030-77497-4
|2 doi
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| 035 |
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|a (OCoLC)1263743387
|z (OCoLC)1263868842
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| 050 |
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|a QA431
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| 072 |
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|a MAT034000
|2 bisacsh
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| 049 |
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|a HCDD
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| 100 |
1 |
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|a Junghanns, Peter,
|d 1953-
|1 https://id.oclc.org/worldcat/entity/E39PBJwhBxMRmY8kjKmcXXvPwC
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| 245 |
1 |
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|a Weighted polynomial approximation and numerical methods for integral equations /
|c Peter Junghanns, Giuseppe Mastroianni, Incoronata Notarangelo.
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| 260 |
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|a Cham, Switzerland :
|b Birkhäuser,
|c 2021.
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| 300 |
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|a 1 online resource
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| 336 |
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|a text
|b txt
|2 rdacontent
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| 337 |
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|a computer
|b c
|2 rdamedia
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| 338 |
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|a online resource
|b cr
|2 rdacarrier
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| 490 |
1 |
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|a Pathways in mathematics
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| 505 |
0 |
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|a Intro -- Preface -- Contents -- 1 Introduction -- 2 Basics from Linear and Nonlinear Functional Analysis -- 2.1 Linear Operators, Banach and Hilbert Spaces -- 2.2 Fundamental Principles -- 2.3 Compact Sets and Compact Operators -- 2.4 Function Spaces -- 2.4.1 Lp-Spaces -- 2.4.2 Spaces of Continuous Functions -- 2.4.3 Approximation Spaces and Unbounded Linear Operators -- 2.5 Fredholm Operators -- 2.6 Stability of Operator Sequences -- 2.7 Fixed Point Theorems and Newton's Method -- 3 Weighted Polynomial Approximation and Quadrature Rules on ( -1,1)
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| 505 |
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|a 3.1 Moduli of Smoothness, K-Functionals, and Best Approximation -- 3.1.1 Moduli of Smoothness and K-Functionals -- 3.1.2 Moduli of Smoothness and Best Weighted Approximation -- 3.1.3 Besov-Type Spaces -- 3.2 Polynomial Approximation with Doubling Weights on the Interval (-1,1) -- 3.2.1 Definitions -- 3.2.2 Polynomial Inequalities with Doubling Weights -- 3.2.3 Christoffel Functions with Respect to Doubling Weights -- 3.2.4 Convergence of Fourier Sums in Weighted Lp-Spaces -- 3.2.5 Lagrange Interpolation in Weighted Lp-Spaces -- 3.2.6 Hermite Interpolation -- 3.2.7 Hermite-Fejér Interpolation
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| 505 |
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|a 3.2.8 Lagrange-Hermite Interpolation -- 3.3 Polynomial Approximation with Exponential Weights on the Interval ( -1,1) -- 3.3.1 Polynomial Inequalities -- 3.3.2 K-Functionals and Moduli of Smoothness -- 3.3.3 Estimates for the Error of Best Weighted Polynomial Approximation -- 3.3.4 Fourier Sums in Weighted Lp-Spaces -- 3.3.5 Lagrange Interpolation in Weighted Lp-Spaces -- 3.3.6 Gaussian Quadrature Rules -- 4 Weighted Polynomial Approximation and Quadrature Rules on Unbounded Intervals -- 4.1 Polynomial Approximation with Generalized Freud Weights on the Real Line -- 4.1.1 The Case of Freud Weights
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| 505 |
8 |
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|a 4.1.2 The Case of Generalized Freud Weights -- 4.1.3 Lagrange Interpolation in Weighted Lp-Spaces -- 4.1.4 Gaussian Quadrature Rules -- 4.1.5 Fourier Sums in Weighted Lp-Spaces -- 4.2 Polynomial Approximation with Generalized Laguerre Weights on the Half Line -- 4.2.1 Polynomial Inequalities -- 4.2.2 Weighted Spaces of Functions -- 4.2.3 Estimates for the Error of Best Weighted Approximation -- 4.2.4 Fourier Sums in Weighted Lp-Spaces -- 4.2.5 Lagrange Interpolation in Weighted Lp-Spaces -- 4.3 Polynomial Approximation with Pollaczek-Laguerre Weights on the Half Line
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| 505 |
8 |
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|a 4.3.1 Polynomial Inequalities -- 4.3.2 Weighted Spaces of Functions -- 4.3.3 Estimates for the Error of Best Weighted Polynomial Approximation -- 4.3.4 Gaussian Quadrature Rules -- 4.3.5 Lagrange Interpolation in L2w -- 4.3.6 Remarks on Numerical Realizations -- Computation of the Mhaskar-Rahmanov-Saff Numbers -- Numerical Construction of Quadrature Rules -- Numerical Examples -- Comparison with the Gaussian Rule Based on Laguerre Zeros -- 5 Mapping Properties of Some Classes of Integral Operators -- 5.1 Some Properties of the Jacobi Polynomials -- 5.2 Cauchy Singular Integral Operators
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| 504 |
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|a Includes bibliographical references and index.
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| 520 |
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|a The book presents a combination of two topics: one coming from the theory of approximation of functions and integrals by interpolation and quadrature, respectively, and the other from the numerical analysis of operator equations, in particular, of integral and related equations. The text focusses on interpolation and quadrature processes for functions defined on bounded and unbounded intervals and having certain singularities at the endpoints of the interval, as well as on numerical methods for Fredholm integral equations of first and second kind with smooth and weakly singular kernel functions, linear and nonlinear Cauchy singular integral equations, and hypersingular integral equations. The book includes both classic and very recent results and will appeal to graduate students and researchers who want to learn about the approximation of functions and the numerical solution of operator equations, in particular integral equations.
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| 650 |
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|a Integral equations
|x Numerical solutions.
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| 650 |
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0 |
|a Approximation theory.
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| 650 |
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7 |
|a Ecuaciones integrales
|x Soluciones numéricas
|2 embne
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| 650 |
0 |
7 |
|a Aproximación, Teoría de
|2 embucm
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| 650 |
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7 |
|a Approximation theory
|2 fast
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| 650 |
|
7 |
|a Integral equations
|x Numerical solutions
|2 fast
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| 700 |
1 |
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|a Mastroianni, G.
|q (Giuseppe)
|1 https://id.oclc.org/worldcat/entity/E39PBJycRmjDHBxt4DBcvGD8YP
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| 700 |
1 |
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|a Notarangelo, Incoronata.
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| 758 |
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|i has work:
|a Weighted polynomial approximation and numerical methods for integral equations (Text)
|1 https://id.oclc.org/worldcat/entity/E39PCGBq3M7hBVCCck9rhGDYHd
|4 https://id.oclc.org/worldcat/ontology/hasWork
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| 776 |
0 |
8 |
|c Original
|z 3030774961
|z 9783030774967
|w (OCoLC)1249077212
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| 830 |
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0 |
|a Pathways in mathematics.
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| 856 |
4 |
0 |
|u https://holycross.idm.oclc.org/login?auth=cas&url=https://link.springer.com/10.1007/978-3-030-77497-4
|y Click for online access
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| 903 |
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|a SPRING-MATH2021
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| 994 |
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|a 92
|b HCD
|