LEADER 10946nam 2200577 450 001 9910556887903321 005 20231110212409.0 010 $a3-030-90951-4 035 $a(MiAaPQ)EBC6941413 035 $a(Au-PeEL)EBL6941413 035 $a(CKB)21435612600041 035 $a(PPN)261518585 035 $a(EXLCZ)9921435612600041 100 $a20221113d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometric approximation theory /$fAlexey R. Alimov and Igor' G. Tsar'kov 210 1$aCham, Switzerland :$cSpringer,$d[2022] 210 4$d©2022 215 $a1 online resource (523 pages) 225 1 $aSpringer Monographs in Mathematics 311 08$aPrint version: Alimov, Alexey R. Geometric Approximation Theory Cham : Springer International Publishing AG,c2022 9783030909505 327 $aIntro -- Preface -- Contents -- 1 Main Notation, Definitions, Auxiliary Results, and Examples -- 1.1 Main Definitions of Geometric Approximation Theory -- 1.2 Preliminaries and Some Facts from Functional Analysis -- 1.3 Elementary Results on Best Approximation. Strictly Convex Spaces. Approximation by Subspaces and Hyperplanes -- 2 Chebyshev Alternation Theorem. Haar's and Mairhuber's Theorems -- 2.1 Chebyshev's and de la Vallée Poussin's Theorems -- 2.2 Solarity and Alternant -- 2.3 Haar's Theorem. Strong Uniqueness of Best Approximation -- 2.4 A Short Note on Extremal Signatures -- 2.5 Mairhuber's Theorem -- 2.6 Approximation of Continuous Functions by Finite-Dimensional Subspaces in the L1-Metric -- 2.7 Remez's Algorithm for Construction of a Polynomials of Near-Best Approximation -- 3 Best Approximation in Euclidean Spaces -- 3.1 Approximation by Convex Sets. Kolmogorov Criterion for a Nearest Element. Deutsch's Lemma -- 3.2 Phelps's Theorem on the Lipschitz Continuity of the Metric Projection onto Chebyshev Sets -- 3.3 Best Least-Squares Polynomial Approximation. Orthogonal Polynomials -- 4 Existence. Compact, Boundedly Compact, Approximatively Compact, and ?-Compact Sets. Continuity of the Metric Projection -- 4.1 Boundedly Compact and Approximatively Compact Sets -- 4.2 Existence of Best Approximation -- 4.3 Approximative ?-Compactness with Respect to Regular ?-Convergence -- 4.3.1 Applications in C[a,b] -- 4.3.2 Applications in Lp -- 5 Characterization of Best Approximation and Solar Properties of Sets -- 5.1 Characterization of an Element of Best Approximation -- 5.2 Suns and the Kolmogorov Criterion for a Nearest Element. Local and Global Best Approximation. Unimodal Sets (LG-Sets) -- 5.3 Kolmogorov Criterion in the Space C(Q) -- 5.4 Continuity of the Metric Projection onto Chebyshev Sets. 327 $a5.5 Differentiability of the Distance Function -- 5.6 Relation of Geometric Approximation Theory to Geometric Optics -- 6 Convexity of Chebyshev Sets and Suns -- 6.1 Convexity of Suns -- 6.2 Convexity of Chebyshev Sets in mathbbRn -- 6.2.1 Berdyshev-Klee-Vlasov's proof -- 6.2.2 Asplund's Proof -- 6.2.3 Konyagin's Proof -- 6.2.4 Vlasov's Proof -- 6.2.5 Brosowski's Proof -- 6.3 The Klee Cavern -- 6.4 Johnson's Example of a Nonconvex Chebyshev Set in an Incomplete Pre-Hilbert Space -- 7 Connectedness and Approximative Properties of Sets. Stability of the Metric Projection and Its Relation to Other Approximative Properties -- 7.1 Classes of Connectedness of Sets -- 7.2 Connectedness of Suns -- 7.3 Dunham's Example of a Disconnected Chebyshev Set with Isolated Point -- 7.4 Klee's Example of a Discrete Chebyshev Set -- 7.5 Koshcheev's Example of a Disconnected Sun -- 7.6 Radial Continuity of the Metric Projection. B-Connectedness of Approximatively Compact Chebyshev Suns -- 7.7 Spans, Segments. Menger Connectedness, and Monotone Path-Connectedness -- 7.7.1 The Banach-Mazur Hull -- 7.7.2 Segments and Spans in Normed Linear Spaces -- 7.7.3 Monotone Path-Connectedness -- 7.8 Continuous and Semicontinuous Selections of Metric Projection. Relation to Solarity and Proximinality of Sets -- 7.9 Suns, Unimodal Sets, Moons, and ORL-Continuity. Brosowski-Wegmann-connectedness -- 7.10 Solarity of the Set of Generalized Rational Fractions -- 7.11 Approximative Properties of Sets Lying in a Subspace -- 7.12 Approximation by Products -- 8 Existence of Chebyshev Subspaces -- 8.1 Chebyshev Subspaces in Finite-Dimensional Spaces -- 8.2 Chebyshev Subspaces in Infinite-Dimensional Spaces -- 8.3 Finite-Dimensional Chebyshev Subspaces in L1(µ). 327 $a9 Efimov-Stechkin Spaces. Uniform Convexity and Uniform Smoothness. Uniqueness and Strong Uniqueness of Best Approximation in Uniformly Convex Spaces -- 9.1 Efimov-Stechkin Spaces -- 9.2 Uniformly Convex Spaces -- 9.3 Uniqueness of Best Approximation by Convex Closed Sets ? -- 9.4 Strong Uniqueness in Uniformly Convex Spaces -- 9.5 Uniformly Smooth Spaces -- 10 Solarity of Chebyshev Sets -- 10.1 Solarity of Boundedly Compact Chebyshev Sets -- 10.2 Relations Between Classes of Suns -- 10.3 Solarity of Chebyshev Sets -- 10.3.1 Solarity of Chebyshev Sets with Continuous Metric Projection -- 10.4 Solarity and Structural Properties of Sets -- 10.4.1 Solarity of Monotone Path-Connected Chebyshev Sets -- 10.4.2 Acyclicity and Cell-Likeness of Sets -- 10.4.3 Solarity of Boundedly Compact P-Acyclic Sets -- 11 Rational Approximation -- 11.1 Existence of a Best Rational Approximation -- 11.2 Characterization of Best Rational Approximation in the Space C[a,b] -- 11.3 Rational Lp-Approximation -- 11.4 Existence of Best Approximation by Generalized Rational Fractions -- 11.5 Characterization of Best Generalized Rational Approximation -- 11.6 Uniqueness of General Rational Approximation -- 11.7 Continuity of the Best Rational Approximation Operator -- 11.8 Notes on Algorithms of Rational Approximations -- 12 Haar Cones and Varisolvency -- 12.1 Properties of Haar Cones. Uniqueness ? -- 12.2 Alternation Theorem for Haar Cones -- 12.3 Varisolvency -- 12.3.1 Uniqueness of Best Approximation by Varisolvent Sets -- 12.3.2 Regular and Singular Points in Approximation by Varisolvent Sets -- 13 Approximation of Vector-Valued Functions -- 13.1 Approximation of Abstract Functions. Interpolation and Uniqueness -- 13.2 Uniqueness of Best Approximation in the Mean for Vector-Valued Functions -- 13.3 On the Haar Condition for Systems of Vector-Valued Functions. 327 $a13.4 Approximation of Vector-Valued Functions by Polynomials -- 13.5 Some Applications of Vector-Valued Approximation -- 14 The Jung Constant -- 14.1 Definition of the Jung Constant -- 14.2 The Measure of Nonconvexity of a Space and the Jung Constant -- 14.3 The Jung Constant and Fixed Points of Condensing and Nonexpansive Maps -- 14.4 On an Approximate Solution of the Equation f(x)=x -- 14.5 On the Jung Constant of the Space ell1n -- 14.6 The Jung Constant and the Jackson Constant -- 14.7 The Relative Jung Constant -- 14.8 The Jung Constant of a Pair of Spaces -- 14.9 Some Remarks on Intersections of Convex Sets. Relation to the Jung Constant -- 15 Chebyshev Centre of a Set. The Problem of Simultaneous Approximation of a Class by a Singleton Set -- 15.1 Chebyshev Centre of a Set -- 15.2 Chebyshev Centres and Spans -- 15.3 Chebyshev Centre in the Space C(Q) -- 15.4 Existence of a Chebyshev Centre in Normed Spaces -- 15.4.1 Quasi-uniform Convexity and Existence of Chebyshev Centres -- 15.5 Uniqueness of a Chebyshev Centre -- 15.5.1 Uniqueness of a Chebyshev Centre of a Compact Set -- 15.5.2 Uniqueness of a Chebyshev Centre of a Bounded Set -- 15.6 Stability of the Chebyshev-Centre Map -- 15.6.1 Stability of the Chebyshev-Centre Map in Arbitrary Normed Spaces -- 15.6.2 Quasi-uniform Convexity and Stability of the Chebyshev-Centre Map -- 15.6.3 Stability of the Chebyshev-Centre Map in Finite-Dimensional Polyhedral Spaces -- 15.6.4 Stability of the Chebyshev-Centre Map in C(Q)-Spaces -- 15.6.5 Stability of the Chebyshev-Centre Map in Hilbert and Uniformly Convex Spaces -- 15.6.6 Stability of the Self-Chebyshev-Centre Map -- 15.6.7 Upper Semicontinuity of the Chebyshev-Centre Map and the Chebyshev-Near-Centre Map -- 15.6.8 Lipschitz Selection of the Chebyshev-Centre Map -- 15.6.9 Discontinuity of the Chebyshev-Centre Map. 327 $a15.7 Characterization of a Chebyshev Centre. Decomposition Theorem -- 15.8 Chebyshev Centres That Are Not Farthest Points -- 15.9 Smooth and Continuous Selections of the Chebyshev-Near-Centre Map -- 15.10 Algorithms and Applied Problems Connected with Chebyshev Centres -- 16 Width. Approximation by a Family of Sets -- 16.1 Problems in Recovery and Approximation Leading to Widths -- 16.2 Definitions of Widths -- 16.3 Fundamental Properties of Widths -- 16.4 Evaluation of Widths of ellp-Ellipsoids -- 16.5 Dranishnikov-Shchepin Widths and Their Relation to the CE-Problem -- 16.6 Bernstein Widths in the Spaces Linfty[0,1] -- 16.7 Widths of Function Classes -- 16.7.1 Definition of the Information Width -- 16.7.2 Estimates for Information Kolmogorov Widths -- 16.7.3 Some Exact Inequalities Between Widths. Projection Constants -- 16.7.4 Some Order Estimates and Duality of Information Width -- 16.7.5 Some Order Estimates for Information Kolmogorov Widths of Finite-Dimensional Balls -- 16.7.6 Order Estimates for Information Kolmogorov Widths of Function Classes -- 16.8 Relation Between the Jung Constant and Widths of Sets -- 16.9 Sequence of Best Approximations -- 17 Approximative Properties of Arbitrary Sets in Normed Linear Spaces. Almost Chebyshev Sets and Sets of Almost Uniqueness -- 17.1 Approximative Properties of Arbitrary Sets -- 17.2 Sets in Strictly Convex Spaces -- 17.3 Constructive Characteristics of Spaces -- 17.4 Sets in Locally Uniformly Convex Spaces -- 17.5 Sets in Uniformly Convex Spaces -- 17.6 Examples -- 17.7 Density and Category Properties of the Sets E(M), AC(M), and T(M) -- 17.8 Category Properties of the Set U(M) -- 17.9 Other Characteristics for the Size of Approximatively Defined Sets -- 17.10 The Farthest-Point Problem -- 17.11 Classes of Small Sets (Zk) -- 17.12 Contingent. 327 $a17.13 Zají?ek-Smallness of the Classes of Sets R(M) and R*(M). 410 0$aSpringer Monographs in Mathematics 606 $aTeoria de l'aproximació$2thub 606 $aSistemes de Txebixov$2thub 606 $aApproximation theory 606 $aApproximation theory$xData processing 608 $aLlibres electrònics$2thub 615 7$aTeoria de l'aproximació 615 7$aSistemes de Txebixov 615 0$aApproximation theory. 615 0$aApproximation theory$xData processing. 676 $a511.4 700 $aAlimov$b Alexey$01266217 702 $aTsar'kov$b Igor' G. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910556887903321 996 $aGeometric approximation theory$92968989 997 $aUNINA LEADER 04692nam 22008295 450 001 9910798557103321 005 20230120074142.0 010 $a0-8232-7369-5 024 7 $a10.1515/9780823273690 035 $a(CKB)3710000000778682 035 $a(EBL)4706317 035 $a(MiAaPQ)EBC4706317 035 $a(MiAaPQ)EBC5046395 035 $a(DE-B1597)555199 035 $a(DE-B1597)9780823273690 035 $a(OCoLC)956320886 035 $a(MiAaPQ)EBC6644644 035 $a(Au-PeEL)EBL6644644 035 $a(MiAaPQ)EBC5846958 035 $a(EXLCZ)993710000000778682 100 $a20200723h20162016 fg 101 0 $aeng 135 $aur|n|---||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aHeidegger, Philosophy, and Politics $eThe Heidelberg Conference /$fPhilippe Lacoue-Labarthe, Hans-Georg Gadamer, Jacques Derrida; Mireille Calle-Gruber 205 $aFirst edition. 210 1$aNew York, NY : $cFordham University Press, $d[2016] 210 4$d©2016 215 $a1 online resource (116 p.) 300 $aDescription based upon print version of record. 311 $a0-8232-7367-9 320 $aIncludes bibliographical references. 327 $tFrontmatter -- $tContents -- $tForeword -- $tPreface -- $tEvent of the archive -- $tConference of February 5, 1988 -- $tMeeting of February 6, 1988 -- $tAppendix: ?like Plato in Syracuse? -- $tNotes 330 $aIn February 1988, philosophers Jacques Derrida, Hans-Georg Gadamer, and Philippe Lacoue-Labarthe came together in Heidelberg before a large audience to discuss the philosophical and political implications of Martin Heidegger?s thought. This event took place in the very amphitheater in which, more than fifty years earlier, Heidegger, as rector of the University of Freiburg and a member of the Nazi Party, had given a speech entitled ?The University in the New Reich.? Heidegger?s involvement in Nazism has always been, and will remain, an indelible scandal, but what is its real relation to his work and thought? And what are the responsibilities of those who read this work, who analyze and elaborate this thought? Conversely, what is at stake in the wholesale dismissal of this important but compromised twentieth-century philosopher?In 1988, in the wake of the recent publication of Victor Farias?s Heidegger and Nazism, and of the heated debates that ensued, these questions had become more pressing than ever. The reflections presented by three of the most prominent of Heidegger?s readers, improvised in French and transcribed here, were an attempt to approach these questions before a broad public, but with a depth of knowledge and a complex sense of the questions at issue that have been often lacking in the press. Ranging over two days and including exchanges with one another and with the audience, the discussions pursued by these major thinkers remain highly relevant today, especially following the publication of Heidegger?s already notorious ?Black Notebooks,? which have added another chapter to the ongoing debates over this contested figure. The present volume recalls a highly charged moment in this history, while also drawing the debate toward its most essential questions. 606 $aDerrida 606 $aFrench philosophy 606 $aGadamer 606 $aHeidegger and nazism 606 $aHeidegger 606 $aLacoue-Labarthe 606 $aphilosophy and politics 606 $aLITERARY CRITICISM / Semiotics & Theory$2bisacsh 610 $aDerrida. 610 $aFrench philosophy. 610 $aGadamer. 610 $aHeidegger and nazism. 610 $aHeidegger. 610 $aLacoue-Labarthe. 610 $aphilosophy and politics. 615 4$aDerrida. 615 4$aFrench philosophy. 615 4$aGadamer. 615 4$aHeidegger and nazism. 615 4$aHeidegger. 615 4$aLacoue-Labarthe. 615 4$aphilosophy and politics. 615 7$aLITERARY CRITICISM / Semiotics & Theory. 676 $a193 700 $aDerrida$b Jacques, $4aut$4http://id.loc.gov/vocabulary/relators/aut$0139765 701 $aFort$b Jeff$01481801 701 $aNancy$b Jean-Luc$0157114 702 $aCalle-Gruber$b Mireille, $4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aGadamer$b Hans-Georg, $4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aLacoue-Labarthe$b Philippe, $4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910798557103321 996 $aHeidegger, Philosophy, and Politics$93853251 997 $aUNINA