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001438847 001__ 1438847
001438847 003__ OCoLC
001438847 005__ 20230309004357.0
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001438847 019__ $$a1263868842
001438847 020__ $$a9783030774974$$q(electronic bk.)
001438847 020__ $$a303077497X$$q(electronic bk.)
001438847 020__ $$z3030774961
001438847 020__ $$z9783030774967
001438847 0247_ $$a10.1007/978-3-030-77497-4$$2doi
001438847 035__ $$aSP(OCoLC)1263743387
001438847 040__ $$aYDX$$beng$$epn$$cYDX$$dGW5XE$$dEBLCP$$dOCLCO$$dOCLCF$$dOCLCQ$$dCOM$$dOCLCO$$dOCLCQ
001438847 049__ $$aISEA
001438847 050_4 $$aQA431
001438847 08204 $$a515/.45$$223
001438847 1001_ $$aJunghanns, Peter,$$d1953-
001438847 24510 $$aWeighted polynomial approximation and numerical methods for integral equations /$$cPeter Junghanns, Giuseppe Mastroianni, Incoronata Notarangelo.
001438847 260__ $$aCham, Switzerland :$$bBirkhäuser,$$c2021.
001438847 300__ $$a1 online resource
001438847 336__ $$atext$$btxt$$2rdacontent
001438847 337__ $$acomputer$$bc$$2rdamedia
001438847 338__ $$aonline resource$$bcr$$2rdacarrier
001438847 4901_ $$aPathways in mathematics
001438847 504__ $$aIncludes bibliographical references and index.
001438847 5050_ $$aIntro -- 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)
001438847 5058_ $$a3.1 Moduli of Smoothness, K-Functionals, and Best Approximation -- 3.1.1 Moduli of Smoothness and K-Functionals -- 3.1.2 Moduli of Smoothness and Best Weighted Approximation -- 3.1.3 Besov-Type Spaces -- 3.2 Polynomial Approximation with Doubling Weights on the Interval (-1,1) -- 3.2.1 Definitions -- 3.2.2 Polynomial Inequalities with Doubling Weights -- 3.2.3 Christoffel Functions with Respect to Doubling Weights -- 3.2.4 Convergence of Fourier Sums in Weighted Lp-Spaces -- 3.2.5 Lagrange Interpolation in Weighted Lp-Spaces -- 3.2.6 Hermite Interpolation -- 3.2.7 Hermite-Fejér Interpolation
001438847 5058_ $$a3.2.8 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
001438847 5058_ $$a4.1.2 The Case of Generalized Freud Weights -- 4.1.3 Lagrange Interpolation in Weighted Lp-Spaces -- 4.1.4 Gaussian Quadrature Rules -- 4.1.5 Fourier Sums in Weighted Lp-Spaces -- 4.2 Polynomial Approximation with Generalized Laguerre Weights on the Half Line -- 4.2.1 Polynomial Inequalities -- 4.2.2 Weighted Spaces of Functions -- 4.2.3 Estimates for the Error of Best Weighted Approximation -- 4.2.4 Fourier Sums in Weighted Lp-Spaces -- 4.2.5 Lagrange Interpolation in Weighted Lp-Spaces -- 4.3 Polynomial Approximation with Pollaczek-Laguerre Weights on the Half Line
001438847 5058_ $$a4.3.1 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
001438847 506__ $$aAccess limited to authorized users.
001438847 520__ $$aThe 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.
001438847 650_0 $$aIntegral equations$$xNumerical solutions.
001438847 650_0 $$aApproximation theory.
001438847 650_6 $$aÉquations intégrales$$xSolutions numériques.
001438847 650_6 $$aThéorie de l'approximation.
001438847 655_0 $$aElectronic books.
001438847 7001_ $$aMastroianni, G.$$q(Giuseppe)
001438847 7001_ $$aNotarangelo, Incoronata.
001438847 77608 $$iPrint version: $$z3030774961$$z9783030774967$$w(OCoLC)1249077212
001438847 830_0 $$aPathways in mathematics.
001438847 852__ $$bebk
001438847 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-77497-4$$zOnline Access$$91397441.1
001438847 909CO $$ooai:library.usi.edu:1438847$$pGLOBAL_SET
001438847 980__ $$aBIB
001438847 980__ $$aEBOOK
001438847 982__ $$aEbook
001438847 983__ $$aOnline
001438847 994__ $$a92$$bISE