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050  4 QA379 -- .M383 2014eb 
082 0  515.48 
100 1  Altomare, Francesco 
245 10 Markov Operators, Positive Semigroups and Approximation 
       Processes 
264  1 Berlin/Boston :|bDe Gruyter, Inc.,|c2014 
264  4 |c©2015 
300    1 online resource (326 pages) 
336    text|btxt|2rdacontent 
337    computer|bc|2rdamedia 
338    online resource|bcr|2rdacarrier 
490 1  De Gruyter Studies in Mathematics Ser. ;|vv.61 
505 0  Intro -- Preface -- Introduction -- Guide to the reader 
       and interdependence of sections -- Notation -- 1 Positive 
       linear operators and approximation problems -- 1.1 
       Positive linear functionals and operators -- 1.1.1 
       Positive Radon measures -- 1.1.2 Choquet boundaries -- 
       1.1.3 Bauer simplices -- 1.2 Korovkin-type approximation 
       theorems -- 1.3 Further convergence criteria for nets of 
       positive linear operators -- 1.4 Asymptotic behaviour of 
       Lipschitz contracting Markov semigroups -- 1.5 Asymptotic 
       formulae for positive linear operators -- 1.6 Moduli of  
       smoothness  and  degree  of approximation by positive 
       linear operators -- 1.7 Notes and comments -- 2 C0-
       semigroups of operators and linear evolution equations -- 
       2.1 C0-semigroups of operators and abstract Cauchy 
       problems -- 2.1.1 C0-semigroups and their generators -- 
       2.1.2 Generation theorems and abstract Cauchy problems -- 
       2.2 Approximation of C0-semigroups -- 2.3 Feller and 
       Markov semigroups of operators -- 2.3.1 Basic properties -
       - 2.3.2 Markov Processes -- 2.3.3 Second-order 
       differential operators on real intervals and Feller theory
       -- 2.3.4 Multidimensional second-order differential 
       operators and Markov semigroups -- 2.4 Notes and comments 
       -- 3 Bernstein-Schnabl operators associated with Markov 
       operators -- 3.1 Generalities, definitions and examples --
       3.1.1 Bernstein-Schnabl operators on [0,1] -- 3.1.2 
       Bernstein-Schnabl operators on Bauer simplices -- 3.1.3 
       Bernstein operators on polytopes -- 3.1.4 Bernstein-
       Schnabl operators associated with strictly elliptic 
       differential operators -- 3.1.5 Bernstein-Schnabl 
       operators associated with tensor products of Markov 
       operators -- 3.1.6 Bernstein-Schnabl operators associated 
       with convex combinations of Markov operators -- 3.1.7 
       Bernstein-Schnabl operators associated with convex 
       convolution products of Markov operators 
505 8  3.2 Approximation properties and rate of convergence -- 
       3.3 Preservation of Hölder continuity -- 3.3.1 Smallest 
       Lipschitz constants and triangles -- 3.3.2 Smallest 
       Lipschitz constants and parallelograms -- 3.4 Bernstein-
       Schnabl operators and convexity -- 3.5 Monotonicity 
       properties -- 3.6 Notes and comments -- 4 Differential 
       operators and Markov semigroups associated with Markov 
       operators -- 4.1 Asymptotic formulae for Bernstein-Schnabl
       operators -- 4.2 Differential operators associated with 
       Markov operators -- 4.3 Markov semigroups generated by 
       differential operators associated with Markov operators --
       4.4 Preservation properties and asymptotic behaviour -- 
       4.5 The special case of the unit interval -- 4.5.1 
       Degenerate differential operators on [0,1] -- 4.5.2 
       Approximation properties by means of Bernstein-Schnabl 
       operators -- 4.5.3 Preservation properties and asymptotic 
       behaviour -- 4.5.4 The saturation class of Bernstein-
       Schnabl operators and the Favard class of their limit 
       semigroups -- 4.6 Notes and comments -- 5 Perturbed 
       differential operators and modified Bernstein-Schnabl 
       operators -- 5.1 Lototsky-Schnabl operators -- 5.2 A 
       modification of Bernstein-Schnabl operators -- 5.3 
       Approximation properties -- 5.4 Preservation properties --
       5.5 Asymptotic formulae -- 5.6 Modified Bernstein-Schnabl 
       operators and first-order perturbations -- 5.7 The unit 
       interval -- 5.7.1 Complete degenerate second-order 
       differential operators on [0, 1] -- 5.7.2 Approximation 
       properties by means of modified Bernstein-Schnabl 
       operators -- 5.8 The d-dimensional simplex and hypercube -
       - 5.9 Notes and comments -- Appendices -- A.1 A 
       classification of Markov operators on two dimensional 
       convex compact subsets -- A.2 Rate of convergence for the 
       limit semigroup of Bernstein operators -- Bibliography -- 
       Symbol index -- Index -- Leere Seite 
520    The series is devoted to the publication of monographs and
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588    Description based on publisher supplied metadata and other
       sources 
590    Electronic reproduction. Ann Arbor, Michigan : ProQuest 
       Ebook Central, 2020. Available via World Wide Web. Access 
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650  0 Boundary value problems.;Differential 
       operators.;Semigroups.;Markov operators 
655  4 Electronic books 
700 1  Cappelletti, Mirella 
700 1  Leonessa, Vita 
700 1  Rasa, Ioan 
776 08 |iPrint version:|aAltomare, Francesco|tMarkov Operators, 
       Positive Semigroups and Approximation Processes|dBerlin/
       Boston : De Gruyter, Inc.,c2014|z9783110372748 
830  3 De Gruyter Studies in Mathematics Ser 
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