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000780628 020__ $$a9783319492421$$q(electronic book)
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000780628 24500 $$aProgress in approximation theory and applicable complex analysis :$$bin memory of Q.I. Rahman /$$cNarendra Kumar Govil, Ram Mohapatra, Muhammed A. Qazi, Gerhard Schmeister, editors.
000780628 264_1 $$aCham, Switzerland :$$bSpringer,$$c[2017]
000780628 264_4 $$c©2017
000780628 300__ $$a1 online resource :$$billustrations.
000780628 336__ $$atext$$btxt$$2rdacontent
000780628 337__ $$acomputer$$bc$$2rdamedia
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000780628 4901_ $$aSpringer optimization and its applications ;$$vvolumes 117
000780628 504__ $$aIncludes bibliographical references.
000780628 5058_ $$a3 Lemmas for Theorem 2.14 Lemmas for Theorem 2.7; 5 Proofs; References; On Bernstein-Type Inequalities for the Polar Derivativeof a Polynomial; 1 Introduction; 2 Bounds on the Uniform Norm of Polar Derivative of a Polynomial; 2.1 Inequalities for Polynomials with no Restriction on Their Zeros; 2.2 Inequalities for Polynomials Having no Zeros in a Circle; 2.3 Inequalities for Polynomials Having all Their Zeros in a Circle; 3 Bounds on the Integral Mean Values of Polar Derivative of a Polynomial; 3.1 Inequalities for Polynomials with no Restriction on Their Zeros
000780628 5058_ $$a3.2 Inequalities for Polynomials Having no Zeros in a Circle3.3 Inequalities for Polynomials Having all Their Zeros in a Circle; References; On Two Inequalities for Polynomials in the Unit Disk; 1 Introduction; 2 Background Material; 3 Theorem 1.1 Implies Theorem 1.2; 4 Cases of Equality; References; Inequalities for Integral Norms of Polynomials via Multipliers; 1 The Schur-Szegő Composition and Polynomial Inequalities; 2 Polynomial Inequalities in Bergman Spaces; 3 Proofs; References; Some Rational Inequalities Inspired by Rahman's Research; 1 General Introduction
000780628 5058_ $$a2 Bernstein-Type Inequalities for Rational Functions with Prescribed Poles3 Comparison Inequalities; 4 Comparison Inequality for Rational Functions; 5 An Inequality of De Bruijn; 6 An Integral Formula; 7 Proofs of Theorems 5-7 and 10 in Sect.2; 8 Proof of Theorem 16 in Sect.4; 9 Proof of Theorem 18 in Sect.5; References; On an Asymptotic Equality for Reproducing Kernels and Sums of Squares of Orthonormal Polynomials; 1 Introduction; 2 Weights on [ -1,1] ; 3 Even Weights on ( -∞,∞) ; 4 The Non-Even, Not Necessarily Unbounded Case; References
000780628 5058_ $$aTwo Walsh-Type Theorems for the Solutions of Multi-Affine Symmetric Polynomials1 Introduction; 2 Solutions of the Polarization of a Complex Polynomial; 3 Loci and Extended Loci of Complex Polynomials; 3.1 Examples of Loci; 4 Argument Coincidence Theorem; References; Vector Inequalities for a Projection in Hilbert Spaces and Applications; 1 Introduction; 2 Vector Inequalities for a Projection; 3 Inequalities for Norm and Numerical Radius; References; A Half-Discrete Hardy-Hilbert-Type Inequality with a Best Possible Constant Factor Related to the Hurwitz Zeta Function; 1 Introduction
000780628 506__ $$aAccess limited to authorized users.
000780628 520__ $$aCurrent and historical research methods in approximation theory are presented in this book beginning with the 1800s and following the evolution of approximation theory via the refinement and extension of classical methods and ending with recent techniques and methodologies. Graduate students, postdocs, and researchers in mathematics, specifically those working in the theory of functions, approximation theory, geometric function theory, and optimization will find new insights as well as a guide to advanced topics. The chapters in this book are grouped into four themes; the first, polynomials (Chapters 1 8), includes inequalities for polynomials and rational functions, orthogonal polynomials, and location of zeros. The second, inequalities and extremal problems are discussed in Chapters 9 13. The third, approximation of functions, involves the approximants being polynomials, rational functions, and other types of functions and are covered in Chapters 14 19. The last theme, quadrature, cubature and applications, comprises the final three chapters and includes an article coauthored by Rahman. This volume serves as a memorial volume to commemorate the distinguished career of Qazi Ibadur Rahman (19342013) of the Universit de Montral. Rahman was considered by his peers as one of the prominent experts in analytic theory of polynomials and entire functions. The novelty of his work lies in his profound abilities and skills in applying techniques from other areas of mathematics, such as optimization theory and variational principles, to obtain final answers to countless open problems.
000780628 588__ $$aOnline resource; title from PDF title page (viewed April 7, 2017)
000780628 60010 $$aRahman, Qazi Ibadur.
000780628 650_0 $$aApproximation theory.
000780628 7001_ $$aGovil, N. K.$$q(Narendra Kumar),$$eeditor.
000780628 7001_ $$aMohapatra, Ram N.,$$eeditor.
000780628 7001_ $$aQazi, Mohammed A.,$$eeditor.
000780628 7001_ $$aSchmeisser, Gerhard,$$eeditor.
000780628 77608 $$iPrint version:$$z3319492403$$z9783319492407$$w(OCoLC)960837823
000780628 830_0 $$aSpringer optimization and its applications ;$$vv. 117.
000780628 852__ $$bebk
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