Szegő's Theorem and Its Descendants (eBook)

Spectral Theory for L2 Perturbations of Orthogonal Polynomials

Barry Simon (Autor)

eBook Download: EPUB

2010
664 Seiten
Princeton University Press (Verlag)
978-1-4008-3705-2 (ISBN)

Infos

This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gabor Szego's classic 1915 theorem and its 1920 extension. Barry Simon emphasizes necessary and sufficient conditions, and provides mathematical background that until now has been available only in journals. Topics include background from the theory of meromorphic functions on hyperelliptic surfaces and the study of covering maps of the Riemann sphere with a finite number of slits removed. This allows for the first book-length treatment of orthogonal polynomials for measures supported on a finite number of intervals on the real line. In addition to the Szego and Killip-Simon theorems for orthogonal polynomials on the unit circle (OPUC) and orthogonal polynomials on the real line (OPRL), Simon covers Toda lattices, the moment problem, and Jacobi operators on the Bethe lattice. Recent work on applications of universality of the CD kernel to obtain detailed asymptotics on the fine structure of the zeros is also included. The book places special emphasis on OPRL, which makes it the essential companion volume to the author's earlier books on OPUC.

Autor

Barry Simon is the IBM Professor of Mathematics and Theoretical Physics at the California Institute of Technology. His books include Methods of Modern Mathematical Physics and Orthogonal Polynomials on the Unit Circle.

Produkt-Details

• Erscheint lt. Verlag: 8.11.2010
• Reihe/Serie: Porter Lectures
• Reihe/Serie: Porter Lectures
• Zusatzinfo: 8 line illus.
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• Themenwelt: Technik
• Schlagworte: Abel's theorem • absolute continuity • Almost periodic function • analytic continuation • analytic function • Approximation • Argument principle • Asymptote • Big O notation • bijection • Blaschke product • Boundary value problem • bounded function • Branch point • Calculation • Cauchy–Schwarz inequality • Chebyshev Polynomials • coefficient • Compact space • continuous function • corollary • Covering space • Degeneracy (mathematics) • Density theorem • Determinant • Dimension • direct sum • Dirichlet problem • discriminant • Division by zero • Eigenfunction • Eigenvalues and Eigenvectors • elliptic function • Entire function • Equation • equivalence class • essential spectrum • existential quantification • Floquet theory • Fourier transform • Fuchsian group • Function (mathematics) • Fundamental domain • Green's Function • Harmonic Measure • hilbert space • integrable system • Interval (mathematics) • Inverse function • Jacobi matrix • Jost function • Kullback–Leibler divergence • Lebesgue measure • Lecture • Limit point • Mathematical Induction • Meromorphic Function • Moment problem • monic polynomial • Monotonic Function • orthogonality • orthogonal polynomials • Parameter • Parity (mathematics) • Plancherel theorem • Pointwise • Poisson Bracket • polynomial • Potential Theory • probability measure • Product topology • Projection (linear algebra) • QR algorithm • QR decomposition • Riemann Mapping Theorem • Riemann sphere • Riemann surface • Schur function • Schwarz lemma • Semi-continuity • Smoothness • Special case • Spectral Theorem • spectral theory • SUBGROUP • Subset • Summation • Support (mathematics) • Symplectic Manifold • Taylor series • Theorem • Toda lattice • Topology of uniform convergence • torus • Trace class • transfer matrix • Triangular Matrix • uniform convergence • Upper half-plane • Variable (mathematics)
• ISBN-10: 1-4008-3705-7 / 1400837057
• ISBN-13: 978-1-4008-3705-2 / 9781400837052