
	Where results make sense

Topic: Spectral theory

Related Topics

Spectral theorem

List of functional analysis topics

Gelfand representation

	INI Workshop - Spectral Theory and its Applications
		Spectral Theory is a vast area of research bringing together different parts of Mathematics and Physics.
		In Mathematics it is Spectral Geometry, which links spectral properties of elliptic operators and related properties of parabolic operators to the geometry and topology of the underlying manifold.
		In Physics methods of Spectral Theory are instrumental in the study of many fundamental results in solid states physics, statistical physics, quantum mechanics and large particle systems.
	www.newton.cam.ac.uk /programmes/STP/stpw01.html (322 words)

	Spectral theory - Wikipedia, the free encyclopedia
		In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix.
		The original spectral theorem was therefore conceived as a version of the theorem on principal axes of an ellipsoid, in an infinite-dimensional setting.
		After Hilbert's initial formulation, the later development of abstract Hilbert space and the spectral theory of a single normal operator on it did very much go in parallel with the requirements of physics; particularly at the hands of von Neumann.
	en.wikipedia.org /wiki/Spectral_theory (299 words)

	STT (Site not responding. Last check: 2007-10-21)
		Spectral Thought Theory has its historical roots in the study of the ordinary consciousness and comprehension, viewed holistically, yet addresses such questions as those dealing with the divisibility and control of one consciousness by another.
		According to quantum field theory, Josephson junctions generate fields of quantum potentials (consisting of a magnetic vector potential and an electrostatic scalar potential), which in turn modulate the connection between the correlated superconductors or cellular systems.
		Spectral patterns of specific frequency associated with nerve firings would impart information to the field, and the field in turn would impose coherence on the ongoing nerve firings.
	www.specmind.com /spectral_mindustries_soliloquy.htm (2701 words)

	Spectral Theory Network (Site not responding. Last check: 2007-10-21)
		The objective of the network is to bring together groups in the UK interested in both pure and applied spectral theory of differential equations, and scientists whose interests lie in the numerical analysis and scientific computations associated with spectral problems, with the goal of producing greater synergy.
		These groups represent diverse aspects of spectral theory: both pure and applied, and both direct and inverse.
		It is recognised that there are other groups in the UK also working on spectral problems and we have the agreement of most of these to be part of the network.
	www.cs.cf.ac.uk /STNetwork/index.html (325 words)

	Giniatoulline, AN INTRODUCTION TO SPECTRAL THEORY
		Chapters 2 and 3 are devoted to the symbiosis of the theory of compact operators in Hilbert spaces and the study of boundary-value problems for elliptic differential equations.
		Chapter 4 is dedicated to the integral representation of self-adjoint operators in the form of Stieltjes integral with respect to the spectral measure.
		Chapters 5 and 6 deal with the explicit spectral decomposition of the Laplacian in L2 and the study of the structure of the Laplacian acting in the whole space.
	edwardspub.com /books/099 (643 words)

	Spectral theory of 1D Schrödinger operators
		The purpose of the Summer School is twofold: on the one hand participants will learn about the mathematical subject, which is spectral theory of Schrödinger operators in one dimension.
		This also means that we will not devellop every detail of the theory, and we will have to take some of the results and implications quoted in the papers as granted without full explanation.
		Spectral theory of this operator is largely about eigenvalues and eigenfunctions of this operator.
	www.math.ucla.edu /~thiele/workshop/subject (310 words)

	General Spectral Theory (Site not responding. Last check: 2007-10-21)
		DC MetaData for: Spectral Theory for Periodic Schrödinger Operators with Reflect...
		Spectral theory and limit theorems for geometrically ergodic Markov processes, I...
		Localization in the Spectral Theory of Operators on Banach Spaces...
	www.scienceoxygen.com /math/647.html (147 words)

	Spectral Theory of the Riemann Zeta-Function - Cambridge University Press
		This is achieved by the use of standard tools from analysis rather than any heavy machinery, forging a substantial aid for beginners in spectral theory as well.
		These ideas are then utilised to unveil a new image of the zeta-function, first perceived by the author, revealing it to be the main gem of a necklace composed of all automorphic L-functions.
		In this book, readers will find a detailed account of one of the most fascinating stories in the recent development of number theory, namely the fusion of two main fields in mathematics that were previously studied separately.
	www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0521445205 (266 words)

	Spectral theory for unbounded self-adjoint operators (Site not responding. Last check: 2007-10-21)
		The spectral theory for unbounded self-adjoint operators on a Hilbert space is an indispensable tool for a variety of problems in mathematical physics.
		The main point of spectral theory is to diagonalize operators.
		Our proof is based on spectral theory for bounded normal operators as developed in the course Analysis 2, in particular the notion of integration with respect to a family of spectral projections.
	www.imf.au.dk /da/uddannelse/studord/older/F2002/node23.html (279 words)

	Category:Spectral theory - Wikipedia, the free encyclopedia
		In mathematics, spectral theory deals with attempts to understand operators, graphs and dynamical systems by means of the spectrum of eigenvalues associated with the system.
		The classical examples of spectra are the vibration modes of a violin string or the spectrum of a hydrogen atom.
		For more information, see the article about Spectral theory.
	en.wikipedia.org /wiki/Category:Spectral_theory (90 words)

	Spectral theory (Site not responding. Last check: 2007-10-21)
		The spectral theory for unbounded self-adjoint operators on a Hilbert space is an indispensable tool for a large number of problems in mathematical physics.
		Then we study two versions of the spectral theorem, one on the functional calculus form and the other on multiplication operator form.
		Here we shall rely on the spectral theory for bounded self-adjoint operators as developed in the course Analysis 2, in particular the notion of integration with respect to a family of spectral projections.
	www.imf.au.dk /da/uddannelse/studord/older/F2001/node19.html (311 words)

	Learn more about Linear algebra in the online encyclopedia. (Site not responding. Last check: 2007-10-21)
		Since linear algebra is a successful theory, its methods have been developed in other parts of mathematics.
		In module theory one replaces the field of scalars by a ring.
		In the spectral theory of operators control of infinite-dimensional matrices is gained, by applying mathematical analysis in a theory that isn't purely algebraic.
	www.onlineencyclopedia.org /l/li/linear_algebra_1.html (809 words)

	Spectral theory of boundary value problems for Dirac type operators - uning, Lesch (ResearchIndex)
		Spectral theory of boundary value problems for Dirac type operators (1999)
		Abstract: The purpose of this note is to describe a unified approach to the fundamental results in the spectral theory of boundary value problems, restricted to the case of Dirac type operators.
		In the applications we describe how Cauchy wavelet analysis works in the theory of elliptic di erential operators on manifolds.
	citeseer.ist.psu.edu /uning99spectral.html (434 words)

	OUP: Introduction to Local Spectral Theory: Laursen
		Modern local spectral theory is built on the classical spectral theorem, a fundamental result in single-operator theory and Hilbert spaces.
		It is highlighted by many characterizations of decomposable operators, and of other related, important classes of operators, as well as an in-depth study of their spectral properties, including identifications of distinguished parts, and results on permanence properties of spectra with respect to several types of similarity.
		Also found is a thorough and quite elementary treatment of the modern single- operator duality theory; this theory has many applications, both to general issues of classification and to such celebrated problems as the invariant subspace problems.
	www.oup.co.uk /isbn/0-19-852381-5 (430 words)

	Spectral Graph Theory and Applications, ALADDIN Center
		Spectral Graph Theory or Algebraic Graph Theory, as it is also known, is the study of the relationship between the eigenvalues and eigenvectors of graphs and their combinatorial properties.
		Random walks on graphs, expander graphs, clustering, and several other combinatorial aspects of graphs are intimately connected to their spectral properties.
		This PROBE brings together researchers from a wide range of disciplines, including machine learning, algorithms, computer science theory, Internet search, human computation, numerical analysis, and materials science.
	www.aladdin.cs.cmu.edu /probes/ongoing_probes/spectral.html (251 words)

	Workshop on Spectral Theory and Automorphic Forms
		In the last 40 years it has been understood that there is a close connection between the spectral theory of hyperbolic manifolds and the theory of L-functions attached to automorphic forms.
		One of the most fruitful approaches to the study of statistical properties of zeros of L-functions involves establishing connections with random matrix theory.
		The goal of this workshop is to bring together leading researchers in those fields, to introduce young researchers and graduate students to the state of the art results and to give an account of applications of techniques from analytic number theory to problems in analysis.
	www.crm.umontreal.ca /Forms04/indexen.html (216 words)

	Spectral Theory and Differential Operators - Cambridge University Press
		This book is an introduction to the theory of partial differential operators.
		However, it describes the theory of Fourier transforms and distributions as far as is needed to analyse the spectrum of any constant coefficient partial differential operator.
		A completely new proof of the spectral theorem for unbounded self-adjoint operators is followed by its application to a variety of second-order elliptic differential operators, from those with discrete spectrum to Schrödinger operators acting on L2(RN).
	www.cambridge.org /catalogue/catalogue.asp?isbn=0521587107 (324 words)

	Method of Spectral Mappings in the Inverse Problem Theory
		Inverse problems of spectral analysis consist in recovering operators from their spectral characteristics.
		This monograph deals with inverse problems of spectral analysis for ordinary differential equations and aims to present the main results on inverse spectral problems using the so-called method of spectral mappings, which is one of the main tools in inverse spectral theory.
		In this chapter the author introduces the so-called Weyl matrix, which is a generalization of the classical Weyl function for the selfadjoint second-order differential operator.
	www.brill.nl /product.asp?ID=10383 (263 words)

	Spectral Lines
		The colored lines (or Spectral Lines) are a kind of "signature" for the atoms.
		Each of these lights has a different spectral "signature", and you can tell what kind of lamp it is by its spectral lines.
		Spectroscopy (this page is currently under construction) is the science of using spectral lines to figure out what something is made of.
	www.colorado.edu /physics/2000/quantumzone (361 words)

	Spectral theory of polynomial matrices (Site not responding. Last check: 2007-10-21)
		Definition 7.2 The pair (X,J) is called (finite) spectral pair and contains all spectral data.
		Due to the block structure the k-th power of J is obtained by taking the k-th power of each individual Jordan cell.
		All in all the spectral data of a polynomial matrix
	www.gang.umass.edu /~kilian/mathesis/node8.html (299 words)

	A New Approach To Inverse Spectral Theory, I. Fundamental Formalism (ResearchIndex)
		Abstract: We present a new approach (distinct from Gel'fand-Levitan) to the theorem of Borg-Marchenko that the m-function (equivalently, spectral measure) for a finite interval or half-line Schrodinger operator determines the potential.
		11 functions and inverse spectral analysis for finite and semi-..
		Modified Prüfer And EFGP Transforms And The Spectral..
	citeseer.ist.psu.edu /468669.html (427 words)

	Spectral Graph Theory, a book by Fan Chung (Site not responding. Last check: 2007-10-21)
		This monograph is an intertwined tale of eigenvalues and their use in unlocking a thousand secrets about graphs.
		The stories will be told --- how the spectrum reveals fundamental properties of a graph, how spectral graph theory links the discrete universe to the continuous one through geometric, analytic and algebraic techniques, and how, through eigenvalues, theory and applications in communications and computer science come together in symbiotic harmony.
		Since spectral graph theory has been evolving very rapidly, the above goals can only be partially fulfilled here.
	math.ucsd.edu /~fan/outline.html (167 words)

	Amazon.com: Books: Spectral Graph Theory (CBMS Regional Conference Series in Mathematics, No. 92) (Cbms Regional ... (Site not responding. Last check: 2007-10-21)
		Graph Theory (Graduate Texts in Mathematics) by Reinhard Diestel
		Beautifully written and elegantly presented, this book is based on 10 lectures given at the CBMS workshop on spectral graph theory in June 1994 at Fresno State University.
		Chung's well-written exposition can be likened to a conversation with a good teacher--one who not only gives you the facts, but tells you what is really going on, why it is worth doing, and how it is related to familiar ideas in other areas.
	www.amazon.com /exec/obidos/tg/detail/-/0821803158?v=glance (570 words)

	2-Spectral Theory, Part I \| The String Coffee Table
		This condition is reminiscent of the condition on ordinary operators to be (semi)-normal.
		Apart from possibly being an interesting question by itself, we may also try to see if the condition to be found here has maybe already arisen in some guise in 2D field theory.
		If it really implies a categorified spectral decomposition as in Hecke operator theory, I don’t know yet.
	golem.ph.utexas.edu /string/archives/000821.html (1771 words)

	MATHnetBASE: Mathematics Online
		This Research Note addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure of the set of zeroes of a general class of nonlinear operators.
		It features the construction of an optimal algebraic/analytic invariant for calculating the Leray-Schauder degree, new methods for solving nonlinear equations in Banach spaces, and general properties of components of solutions sets presented with minimal use of topological tools.
		Appealing to a broad audience, Spectral Theory and Nonlinear Functional Analysis contains many important contributions to linear algebra, linear and nonlinear functional analysis, and topology and opens the door for further advances.
	www.mathnetbase.com /ejournals/books/book_summary/summary.asp?id=1033 (186 words)

	Course 321 - Modern Analysis: Linear Spaces, Linear Operators, Spectral Theory (Site not responding. Last check: 2007-10-21)
		Introduction: Linear algebra, matrices and linear operators on finite dimensional vector spaces, eigenvalue theory.
		Spectral Theory: Spectrum, resolvent spectral radius, applications of vector valued analytic function theory, operational calculus, spectral theorem.
		Banach Algebras: Definition, examples, Gelfand representation, spectral theorem for normal operators.
	www.maths.tcd.ie /pub/official/Courses/321in9697.html (154 words)

	Lyapunov Spectral Intervals: Theory and Computation
		Lyapunov Spectral Intervals: Theory and Computation: SIAM Journal on Numerical Analysis Vol.
		Different definitions of spectra have been proposed over the years to characterize the asymptotic behavior of nonautonomous linear systems.
		By using an orthogonal change of variables transforming the system to upper triangular form, and the assumption of integral separation for the diagonal of the new triangular system, we justify how popular numerical methods, the so-called continuous QR and SVD approaches, can be used to approximate these spectra.
	epubs.siam.org /sam-bin/dbq/article/39230 (207 words)

Try your search on: Qwika (all wikis)