LEADER 05372nam 2200661 a 450 001 9910458707303321 005 20200520144314.0 010 $a1-280-63062-0 010 $a9786610630622 010 $a0-08-045592-1 035 $a(CKB)1000000000364413 035 $a(EBL)269969 035 $a(OCoLC)476000443 035 $a(SSID)ssj0000171228 035 $a(PQKBManifestationID)12036780 035 $a(PQKBTitleCode)TC0000171228 035 $a(PQKBWorkID)10236411 035 $a(PQKB)10115679 035 $a(MiAaPQ)EBC269969 035 $a(PPN)170240827 035 $a(Au-PeEL)EBL269969 035 $a(CaPaEBR)ebr10138186 035 $a(CaONFJC)MIL63062 035 $a(OCoLC)437172632 035 $a(EXLCZ)991000000000364413 100 $a20051121d2005 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aHilbert spaces with applications$b[electronic resource] /$fLokenath Debnath, Piotr Mikusin?ski 205 $a3rd. ed. 210 $aAmsterdam ;$aBoston $cElsevier Academic Press$dc2005 215 $a1 online resource (599 p.) 300 $aDescription based upon print version of record. 311 $a0-12-208438-1 320 $aIncludes bibliographical references (p. 565-569) and index. 327 $aContents; Preface to the Third Edition; Preface to the Second Edition; Preface to the First Edition; Normed Vector Spaces; Introduction; Vector Spaces; Normed Spaces; Banach Spaces; Linear Mappings; Banach Fixed Point Theorem; Exercises; The Lebesgue Integral; Introduction; Step Functions; Lebesgue Integrable Functions; The Absolute Value of an Integrable Function; Series of Integrable Functions; Norm in L1(R); Convergence Almost Everywhere; Fundamental Convergence Theorems; Locally Integrable Functions; The Lebesgue Integral and the Riemann Integral; Lebesgue Measure on R 327 $aComplex-Valued Lebesgue Integrable FunctionsThe Spaces Lp(R); Lebesgue Integrable Functions on RN; Convolution; Exercises; Hilbert Spaces and Orthonormal Systems; Introduction; Inner Product Spaces; Hilbert Spaces; Orthogonal and Orthonormal Systems; Trigonometric Fourier Series; Orthogonal Complements and Projections; Riesz Representation Theorem; Exercises; Linear Operators on Hilbert Spaces; Introduction; Examples of Operators; Bilinear Functionals and Quadratic Forms; Adjoint and Self-Adjoint Operators; Normal, Isometric, and Unitary Operators; Positive Operators; Projection Operators 327 $aCompact OperatorsEigenvalues and Eigenvectors; Spectral Decomposition; Unbounded Operators; Exercises; Applications to Integral and Differential Equations; Introduction; Basic Existence Theorems; Fredholm Integral Equations; Method of Successive Approximations; Volterra Integral Equations; Method of Solution for a Separable Kernel; Abel's Integral Equation; Ordinary Differential Equations; Sturm-Liouville Systems; Inverse Differential Operators; The Fourier Transform; Applications of the Fourier Transform; Exercises; Generalized Functions and Partial Differential Equations; Introduction 327 $aDistributionsSobolev Spaces; Fundamental Solutions; Elliptic Boundary Value Problems; Applications of the Fourier Transform; Exercises; Mathematical Foundations of Quantum Mechanics; Introduction; Basic Concepts and Equations; Postulates of Quantum Mechanics; The Heisenberg Uncertainty Principle; The Schro?dinger Equation of Motion; The Schro?dinger Picture; The Heisenberg Picture; The Interaction Picture; The Linear Harmonic Oscillator; Angular Momentum Operators; The Dirac Relativistic Wave Equation; Exercises; Wavelets and Wavelet Transforms; Brief Historical Remarks 327 $aContinuous Wavelet TransformsThe Discrete Wavelet Transform; Multiresolution Analysis; Examples of Orthonormal Wavelets; Exercises; Optimization Problems and Other Miscellaneous Applications; Introduction; The Gateaux and Fre?chet Differentials; Optimization Problems; Minimization of Quadratic Functionals; Variational Inequalities; Optimal Control Problems; Approximation Theory; The Shannon Sampling Theorem; Linear and Nonlinear Stability; Bifurcation Theory; Exercises; Hints and Answers to Selected Exercises; 1.7 Exercises; 2.16 Exercises; 3.8 Exercises; 4.12 Exercises; 5.13 Exercises 327 $a6.7 Exercises 330 $aBuilding on the success of the two previous editions, Introduction to Hilbert Spaces with Applications, 3E, offers an overview of the basic ideas and results of Hilbert space theory and functional analysis. It acquaints students with the Lebesgue integral, and includes an enhanced presentation of results and proofs. Students and researchers will benefit from the wealth of revised examples in new, diverse applications as they apply to optimization, variational and control problems, and problems in approximation theory, nonlinear instability, and bifurcation. The text also includes a popular cha 606 $aHilbert space 608 $aElectronic books. 615 0$aHilbert space. 676 $a515/.733 700 $aDebnath$b Lokenath$042473 701 $aMikusin?ski$b Piotr$0147912 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910458707303321 996 $aHilbert spaces with applications$91981001 997 $aUNINA