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Applied functional analysis / / Jean-Pierre Aubin ; exercises by Bernard Cornet and Jean-Michel Lasry ; translated by Carole Labrousse
Applied functional analysis / / Jean-Pierre Aubin ; exercises by Bernard Cornet and Jean-Michel Lasry ; translated by Carole Labrousse
Autore Aubin Jean Pierre
Edizione [2nd ed.]
Pubbl/distr/stampa New York, New York : , : John Wiley & Sons, Inc., , 2000
Descrizione fisica 1 online resource (520 p.)
Disciplina 515.7
515/.7
Collana Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts
Soggetto topico Functional analysis
Hilbert space
ISBN 1-118-03272-1
1-118-03097-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto APPLIED FUNCTIONAL ANALYSIS; CONTENTS; Preface; Introduction: A Guide to the Reader; 1. The Projection Theorem; 1.1. Definition of a Hilbert Space; 1.2. Review of Continuous Linear and Bilinear Operators; 1.3. Extension of Continuous Linear and Bilinear Operators by Density; 1.4. The Best Approximation Theorem; 1.5. Orthogonal Projectors; 1.6. Closed Subspaces, Quotient Spaces, and Finite Products of Hilbert Spaces; *1.7. Orthogonal Bases for a Separable Hilbert Space; 2. Theorems on Extension and Separation; 2.1. Extension of Continuous Linear and Bilinear Operators; 2.2. A Density Criterion
2.3. Separation Theorems2.4. A Separation Theorem in Finite Dimensional Spaces; 2.5. Support Functions; *2.6. The Duality Theorem in Convex Optimization; *2.7. Von Neumann's Minimax Theorem; *2.8. Characterization of Pareto Optima; 3. Dual Spaces and Transposed Operators; 3.1. The Dual of a Hilbert Space; 3.2. Realization of the Dual of a Hilbert Space; 3.3. Transposition of Operators; 3.4. Transposition of Injective Operators; 3.5. Duals of Finite Products, Quotient Spaces, and Closed or Dense Subspaces; 3.6. The Theorem of Lax-Milgram; *3.7. Variational Inequalities
*3.8. Noncooperative Equilibria in n-Person Quadratic Games4. The Banach Theorem and the Banach-Steinhaus Theorem; 4.1. Properties of Bounded Sets of Operators 7; 4.2. The Mean Ergodic Theorem; 4.3. The Banach Theorem; 4.4. The Closed Range Theorem; 4.5. Characterization of Left Invertible Operators; 4.6. Characterization of Right Invertible Operators; *4.7. Quadratic Programming with Linear Constraints; 5. Construction of Hilbert Spaces; 5.1. The Initial Scalar Product; 5.2. The Final Scalar Product; 5.3. Normal Subspaces of a Pivot Space
5.4. Minimal and Maximal Domains of a Closed Family of Operators*5.5. Unbounded Operators and Their Adjoints; *5.6. Completion of a Pre-Hilbert Space Contained in a Hilbert Space; *5.7. Hausdorff Completion; *5.8. The Hilbert Sum of Hilbert Spaces; *5.9. Reproducing Kernels of a Hilbert Space of Functions 1; 6. L2 Spaces and Convolution Operators; 6.1. The Space L2(Ω) of Square Integrable Functions; 6.2. The Spaces L2(Ω, a) with Weights; 6.3. The Space Hs; 6.4. The Convolution Product for Functions of L0( Rn) and of L1(Rn); 6.5. Convolution Operators; 6.6. Approximation by Convolution
*6.7. Example. Convolution Power for Characteristic Functions*6.8. Example. Convolution Product for Polynomials: Appell Polynomials; 7. Sobolev Spaces of Functions of One Variable; 7.1. The Space H0m(Ω) and Its Dual H-m(Ω); 7.2. Definition of Distributions; 7.3. Differentiation of Distributions; 7.4. Relations Between H0m(Ω) and H0m(R); 7.5. The Sobolev Space Hm(Ω); 7.6. Relations Between Hm(Ω) and Hm(R); *7.7. Characterization of the Dual of Hm(Ω); 7.8. Trace Theorems; 7.9. Convolution of Distributions; 8. Some Approximation Procedures in Spaces of Functions
8.1. Approximation by Orthogonal Polynomials
Record Nr. UNINA-9910141235803321
Aubin Jean Pierre  
New York, New York : , : John Wiley & Sons, Inc., , 2000
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Bifurcation and nonlinear eigenvalue problems : proceedings, Universite de Paris XIII, Villetaneuse, France, October 2-4 1978 / / edited by C. Bardos, J. M. Lasry, M. Schatzman
Bifurcation and nonlinear eigenvalue problems : proceedings, Universite de Paris XIII, Villetaneuse, France, October 2-4 1978 / / edited by C. Bardos, J. M. Lasry, M. Schatzman
Edizione [1st ed. 1980.]
Pubbl/distr/stampa Berlin ; ; Heidelberg : , : Springer-Verlag, , [1980]
Descrizione fisica 1 online resource (X, 298 p.)
Disciplina 515.352
Collana Lecture Notes in Mathematics
Soggetto topico Bifurcation theory
ISBN 3-540-38637-8
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Parameter dependence of solutions of classes of quasi-linear elliptic and parabolic differential equations -- Some applications of the method of super and subsolutions -- Multiple solutions of a bifurcation problem -- On nonlinear eigenvalue problems which extend into free boundaries problems -- aux theories statistiques de la turbulence pleinement developpee -- Experimental study of the mechanism of a new hydrodynamical instability observed at some interfaces between immiscible liquids -- Remarques sur un problème de valeurs propres non linéaires faisant intervenir des fonctions non différentiables -- Solar flares: A non linear eigenvalue problem in an unbounded domain -- Bifurcation of invariant tori in R3 -- Pattern formation and wave propagation in the s-a system -- Variation d'un point de retournement par rapport au domaine -- Dynamic Pade' approximant and behavior singularities in nonlinear physico-chemical systems -- Remarks on a non linear equation arising in population genetics -- Triplets de solutions d'une equation aux derivees partielles elliptique non lineaire.
Record Nr. UNISA-996466636003316
Berlin ; ; Heidelberg : , : Springer-Verlag, , [1980]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui