Hilbert space

About: Hilbert space is a research topic. Over the lifetime, 29705 publications have been published within this topic receiving 637043 citations.

Operator theory in function spaces

Abstract: Bounded linear operators Interpolation of Banach spaces Integral operators on $L^p$ spaces Bergman spaces Bloch and Besov spaces The Berezin transform Toeplitz operators on the Bergman space Hankel operators on the Bergman space Hardy spaces and BMO Hankel operators on the Hardy space Composition operators Bibliography Index.

Solvable Models in Quantum Mechanics

Abstract: Introduction The one-center point interaction: The one-center point interaction in three dimensions Coulomb plus one-center point interaction in three dimensions The one-center $\delta$-interaction in one dimension The one-center $\delta$'-interaction in one dimension The one-center point interaction in two dimensions Point interactions with a finite number of centers: Finitely many point interactions in three dimensions Finitely many $\delta$-interactions in one dimension Finitely many $\delta$'-interactions in one dimension Finitely many point interactions in two dimensions Point interactions with infinitely many centers: Infinitely many point interactions in three dimensions Infinitely many $\delta$-interactions in one dimension Infinitely many $\delta$'-interactions in one dimension Infinitely many point interactions in two dimensions Random Hamiltonians with point interactions Appendices: Self-adjoint extensions of symmetric operators Spectral properties of Hamiltonians defined as quadratic forms Schrodinger operators with interactions concentrated around infinitely many centers Boundary conditions for Schrodinger operators on $(0,\infty)$ Time-dependent scattering theory for point interactions Dirichlet forms for point interactions Point interactions and scales of Hilbert spaces Nonstandard analysis and point interactions Elements of probability theory Relativistic point interactions in one dimension References Author Index Subject Index Seize ans apres Bibliography Errata and addenda.

Spectral theory and differential operators

Abstract: Linear operations in Banach spaces Entropy numbers, s-numbers, and eigenvalues Unbounded linear operators Sesquilinear forms in Hilbert spaces Sobolev spaces Generalized Dirichlet and Neumann boundary-value problems Second-order differential operators on arbitrary open sets Capacity and compactness criteria Essential spectra Essential spectra of general second-order differential operators Global and asymptotic estimates for the eigen-values of - + q when q is real. Estimates for the singular values of - + q when 1 is complete Bibliography Notation index Subject index

Nonlinear semigroups and differential equations in Banach spaces

Abstract: I Preliminaries.- 1. Metric properties of normed spaces.- 1.1 Duality mappings.- 1.2 Strictly convex normed spaces.- 1.3 Uniformly convex Banach spaces.- 2. Vectorial functions defined on real intervals.- 2.1 Absolutely continuous vectorial functions.- 2.2 Vectorial distributions and Wk,p spaces.- 2.3 Sobolev spaces.- 3. Semigroups of continuous linear operators.- 3.1 Semigroups of class (C0). Hille-Yosida theorem.- 3.2 Analytic semigroups.- 3.3 Nonhomogeneous linear differential equations.- II Nonlinear Operators in Banach Spaces.- 1. Maximal monotone operators.- 1.1 Definitions and fundamental concepts.- 1.2 A general perturbation theorem.- 1.3 A nonlinear elliptic boundary problem.- 2. Subdifferential mappings.- 2.1 Lower semicontinuous convex functions.- 2.2 Subdifferentials of convex functions.- 2.3 Some examples of cyclically monotone operators.- 3. Dissipative sets in Banach spaces.- 3.1 Basic properties of dissipative sets.- 3.2 Perturbations of dissipative sets.- 3.3 Riccati equations in Hilbert spaces.- Bibliographical notes.- III Differential Equations in Banach Spaces.- 1. Semigroups of nonlinear contractions in Banach spaces.- 1.1 General properties of nonlinear semigroups.- 1.2 The exponential formula.- 1.3 Convergence theorems.- 1.4 Generation of nonlinear semigroups.- 2. Quasi-autonomous differential equations.- 2.1 Existence theorems.- 2.2 Periodic solutions.- 2.3 Examples.- 3. Differential equations associated with continuous dissipative operators.- 3.1 A general existence result.- 3.2 Continuous perturbations of m-dissipative operators.- 3.3 Semi-linear second-order elliptic equations in L1.- 4. Time-dependent nonlinear differential equations.- 4.1 Evolution equations associated with dissipative sets.- 4.2 Evolution equations associated with nonlinear monotone hemicon-tinuous operators.- Bibliographical notes.- IV Nonlinear Differential Equations in Hilbert Spaces.- 1. Nonlinear semigroups in Hilbert spaces.- 1.1 Nonlinear version of the Hille-Yosida theorem.- 1.2 Exponential formulae.- 1.3 Invariant sets with respect to nonlinear semigroups.- 2. Smoothing effect on initial data.- 2.1 The case in which A = ? ?.- 2.2 The case in which int D(A) ? ?.- 2.3 Applications.- 3. Variational evolution inequations.- 3.1 Unilateral conditions on u(t).- 3.2 Unilateral conditions on $$ \frac{{du}}{{dt}}(t) $$.- 3.3 A class of nonlinear variational inequations.- 3.4 Applications.- 4. Nonlinear Volterra equations with positive kernels in Hilbert spaces.- 4.1 Positive kernels.- 4.2 Equation (4.1) with A = ? ?.- 4.3 Equation (4.1) with A demicontinuous.- 4.4 A class of integro-differential equations.- 4.5 Further investigation of the preceding case.- Bibliographical notes.- V Second Order Nonlinear Differential Equations.- 1. Nonlinear differential equations of hyperbolic type.- 1.1 The equation $$ \frac{{{d^2}u}}{{d{t^2}}} + Au + M\left( {\frac{{du}}{{dt}}} \right) \mathrel\backepsilon f $$.- 1.2 Further investigation of the preceding case.- 1.3 Examples.- 1.4 Singular perturbations and hyperbolic variational inequations.- 1.5 Nonlinear wave equation.- 2. Boundary value problems for second order nonlinear differential equations.- 2.1 A class of two-point boundary value problems.- 2.2 Examples.- 2.3 A boundary value problem on half-axis.- 2.4 The square root of a nonlinear maximal monotone operator.- Bibliographical notes.