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	PlanetMath: semi-Fredholm operator
		A semi-Fredholm operator is a bounded operator between Banach spaces that has a finite dimensional kernel or cokernel, and closed range.
		There are two semigroups of semi-Fredholm operators: upper semi-Fredholm operators (those which have finite dimensional kernels), and lower semi-Fredholm operators (those which have finite dimensional cokernels).
		If an operator is homotopic through (a norm continuous path of) semi-Fredholm operators to a Fredholm operator, then it is Fredholm.
	www.planetmath.org /encyclopedia/SemiFredholmOperator.html (131 words)

	PlanetMath: semi-Fredholm operator
		A semi-Fredholm operator is a bounded operator between Banach spaces that has a finite dimensional kernel or cokernel, and closed range.
		There are two semigroups of semi-Fredholm operators: upper semi-Fredholm operators (those which have finite dimensional kernels), and lower semi-Fredholm operators (those which have finite dimensional cokernels).
		If an operator is homotopic through (a norm continuous path of) semi-Fredholm operators to a Fredholm operator, then it is Fredholm.
	planetmath.org /encyclopedia/SemiFredholmOperator.html (131 words)

	Fredholm operator - Wikipedia, the free encyclopedia
		In mathematics, a Fredholm operator is an operator that arises in the Fredholm theory of integral equations.
		The Fredholm operator is a bounded linear operator between two Banach spaces whose range is closed and whose kernel and cokernel are finite-dimensional.
		The use of Fredholm operators in partial differential equations is an abstract form of the parametrix method.
	en.wikipedia.org /wiki/Fredholm_operator (274 words)

	Proceedings of the American Mathematical Society
		Index of B-Fredholm operators and generalization of a Weyl theorem
		M. Berkani, On a class of quasi-Fredholm operators.
		R. Harte, Invertibility and singularity for bounded linear operators; Marcel Dekker.
	www.ams.org /proc/2002-130-06/S0002-9939-01-06291-8/home.html (239 words)

	PlanetMath: Fredholm operator
		A Fredholm operator is a bounded operator between Banach spaces that has a finite dimensional kernel and cokernel (and closed range).
		Cross-references: adjoint, algebra, vector spaces, compact operators, invertible, range, closed, cokernel, kernel, finite dimensional, Banach spaces, bounded operator
		This is version 10 of Fredholm operator, born on 2002-08-25, modified 2004-06-26.
	planetmath.org /encyclopedia/FredholmOperator.html (80 words)

	Mathematical Papers
		With every Fredholm sequence, there are associated three integers which are the analogues of the nullity, the defiency and the index of a Fredholm operator.
		The nullity of a Fredholm sequence (A_n) is interpreted as a quantity which describes the asymptotic behaviour of the small singular values of the matrices A_n as n tends to infinity, and an identity is derived which allows the computation of this nullity in many situations.
		The topics of this paper are Fredholm properties and the applicability of the finite section method for band operators on l^p-spaces as well as for their norm limits which we call band-dominated operators.
	www.mathematik.tu-darmstadt.de /~roch/Papers.html (2011 words)

	Springer Online Reference Works
		A completely-continuous operator is nowadays usually called a compact operator.
		A Fredholm kernel is a bivalent tensor (cf.
		Fredholm kernels and Fredholm operators constitute a natural domain of application of the Fredholm theory.
	eom.springer.de /F/f041440.htm (308 words)

	Fredholm biography
		He solved his operator equation in the particular cases which arise in the study of the physical problem in his thesis (and in the paper which appeared in 1900 based on that thesis) while the general case was solved by Fredholm somewhat later and not published until 1908.
		Fredholm's work on integral equations was met with great interest and boosted the morale and self-respect of Swedish mathematicians who so far had been working under the shadow of the continental cultural empires Germany and France.
		Fredholm received many honours for his mathematical contributions, including the V A Wallmarks Prize for the theory of differential equations in 1903, the Poncelet Prize from the French
	www-groups.dcs.st-and.ac.uk /~history/Biographies/Fredholm.html (1692 words)

	PlanetMath: Fredholm index
		is a norm continuous path of Fredholm operators, then
		Cross-references: path, continuous, norm, compact operator, vector spaces, finite-dimensional, Fredholm operator
		This is version 5 of Fredholm index, born on 2002-12-30, modified 2004-04-16.
	planetmath.org /encyclopedia/FredholmIndex.html (53 words)

	[No title]
		Homework 3 Multidimensional Fredholm integral equation, resolvent operators and eigenvalues of compact integral operators, non-self adjoint compact operator, and solvability of Ku=f.
		Spectral representations of Operators A LaTeX file for two theorems on the spectral representation of bounded and unbounded operators.
		Separable Fredholm Integral Equations Separable integral equations are equivalent to matrix equations with appropriate definitions.
	www.math.montana.edu /~pernarow/M560/1998/M560.html (663 words)

	Compact operator - Wikipedia, the free encyclopedia
		In functional analysis, a branch of mathematics, a compact operator (or completely continuous operator) is a linear operator L from a Banach space X to another Banach space Y, such that the image under L of any bounded subset of X is a relatively compact subset of Y.
		The origin of the theory of compact operators is in the theory of integral equations.
		The compact operators from a Banach space to itself form a two-sided ideal in the algebra of all bounded operators on the space.
	en.wikipedia.org /wiki/Compact_operator (645 words)

	Directory of open access journals
		Fredholm linear operators associated with ordinary differential equations on noncompact intervals
		In the noncompact interval $J=[a,infty)$ we consider a linear problem of the form $Lx=y,; x in S$, where $L$ is a first order differential operator, $y$ a locally summable function in $J$, and $S$ a subspace of the Fr'{e}chet space of the locally absolutely continuous functions in $J$.
		In the general case, the restriction of $L$ to $S$ is not a Fredholm operator.
	www.doaj.org /doaj?func=abstract&id=89939&recNo=1&toc=1 (220 words)

	Fredholm determinant - Wikipedia, the free encyclopedia
		In mathematics, a Fredholm determinant is a complex analytic function which generalizes the characteristic polynomial of a matrix.
		It is defined for those operators which have continuous kernels, i.e., kernels in the sense of mathematical analysis.
		The trace is well-defined for the Fredholm kernels, since these are trace-class or nuclear operators, which follows from the fact that the Fredholm operator is a compact operator.
	en.wikipedia.org /wiki/Fredholm_determinant (273 words)

	[No title] (Site not responding. Last check: 2007-10-30)
		Fredholm operators are only included to the extent that they were discussed in class.
		You should know that an operator of the form I+K where K is compact has closed range and finite dimensional nullspace.
		You should know that there are many tools from complex analysis that can be applied to resolvent operators (this is an important part of spectral theory) but this is not a core part of the course.
	amath.colorado.edu /courses/5450/2006Spr/midterm1_notes.txt (210 words)

	Preprints
		We use this data to define Toeplitz operators with symbols in the transformation group $C^$-algebra $C(X) \rtimes \Gamma$, and we show that if the symbol of such a Toeplitz operator* is invertible, then the operator is Fredholm.
		We show that the group of automorphisms of $M_n(C(M))$ that respect the unbounded Fredholm module is a compact topological group in the topology of pointwise convergence.
		If $D$ is an operator of Dirac type and we restrict to scalar functions, then this group is also a Lie group.
	www.math.tcu.edu /Preprints/Preprints.html (725 words)

	Transactions of the American Mathematical Society
		Various generalizations to other unbounded domains, higher order operators or elliptic systems are possible and briefly alluded to, but not discussed in detail.
		Browder, F. E., On the spectral theory of elliptic differential operators I, Math.
		Keywords: Fredholm operator, unique continuation, eigenvalue, generalized eigenfunction, exponential decay.
	www.ams.org /tran/2004-356-05/S0002-9947-03-03234-3/home.html (646 words)

	Quantum Hall Conductance
		A second theoretical framework identifies the Hall conductance with a Fredholm index of a certain operator.
		This framework is known to apply to non interacting electrons in two dimensions where the Fredholm operator is constructed from the one particle Schrodinger Hamiltonian of the system.
		The Fredholm framework would be a satisfactory theory of the integer quantum Hall effect if one could remove the restriction of non interacting electrons.
	www.math.princeton.edu /~aizenman/OpenProblems.iamp/9903.QHallCond.html (602 words)

	[No title]
		Analogs of Grobman-Hartman theorem on stable and unstable manifolds solutions for differential equations in Banach spaces with degenerate Fredholm operator at the derivative are proved.
		However, no results of this theory concerning evolution equations with degenerate operator at the derivative are known, though these equations have numerous applications in ﬁltration theory [1], nonlinear waves theory (the Boussinesq-Love equation) [22] and motion theory of non-Newtonian ﬂuids [15].
		The present work, as an introduction to center manifold methods for evolution equations with Fredholm operator at the derivative, considers invariant manifolds technique on the base of the resolving systems theory [13] developed by authors.
	ljm.ksu.ru /vol20/25.xml (752 words)

	[No title]
		] A linear operator between Banach spaces which has closed range, and both the Fredholm operator and its adjoint have finite dimensional null space.
		] In a drilling operation in which a string of pipe has become stuck, a tool that measures the amount of stretch in the stuck string and indicates the deepest point at which the pipe is free.
		] Frequency at which a normally driven oscillator operates in the absence of a driving signal.
	www.accessscience.com /Dictionary/F/F23/DictF23.html (2532 words)

	Publications and Preprints
		We define Toeplitz operators with symbols in the irrational rotation algebras and show that several of the properties of classical Toeplitz operators carry over to this situation.
		A self-adjoint first-order elliptic differential operator $D$ acting on sections of a Hermitian vector bundle over a compact Riemannian manifold $M$ naturally determines an unbounded Fredholm module over $M_n(C(M))$ for each positive integer $n$.
		In this paper, the author studies a class of unbounded Fredholm modules over a reduced group $C^$-algebra, and he shows that the isometry groups of these unbounded Fredholm* modules are always compact Lie groups.
	faculty.tcu.edu /epark/pubs.html (1056 words)

	colloquium: The index of an elliptic differential operator.
		In functional analysis several classes of bounded operators have recieved special attention.
		To each Fredholm operator one assigns a so-called index.
		\noindent It turns out that certain partial differential operators (the elliptic ones) are Fredholm operators - at least when the operators are considered on a compact Riemannian manifold without boundary.
	www2.mat.dtu.dk /events/uk?id=68 (144 words)

	K-Theory for Dummies, II \| The String Coffee Table
		One of the crucial keys for unlocking the above dictionary is the fact that the tachyon field operators that we are talking about indeed are Dirac operators in situations where they describe “geometric” D-branes.
		Dividing out the space of Fredholm modules by these three equivalence relations, following the above dictionary, yields the K-homology group, and our D-brane defines a class of that.
		-bimodule with a Fredholm operator represented on it.
	golem.ph.utexas.edu /string/archives/000880.html (1233 words)

	Biologie - Fredholm-Operator
		Fredholm) eine Verallgemeinerung der Invertierbarkeit einer linearen Abbildung zwischen Vektorräumen.
		Für jeden Fredholm-Operator A und jeden kompakten Operator K ist A + K ebenfalls ein Fredholm-Operator mit selbem Fredholm-Index wie A.
		Insbesondere ist jede kompakte Störung der Identität, also jeder Operator der Form I + K für einen kompakten Operator K ein Fredholm-Operator vom Index 0.
	www.biologie.de /biowiki/Fredholm-Operator (236 words)

	Fredholm Alternative -- from Wolfram MathWorld
		compact operator, such as an integral operator with a smooth integral kernel.
		The Fredholm alternative can be restated as follows: any nonzero
		Fredholm Operator, Integral Kernel, Invertible Matrix, Spectral Theory.
	mathworld.wolfram.com /FredholmAlternative.html (69 words)

	Gilkey: Invariance Theory, ... (Site not responding. Last check: 2007-10-30)
		Copies of this second edition are still available directly from Peter B. Gilkey at US$ 60 per copy.
		Fredholm Operators and the Index of a Fredholm Operator
		Local Formula for the Index of an Elliptic Operator
	www.emis.de /monographs/gilkey (208 words)

	K-theory for dummies, I \| The String Coffee Table
		A Fredholm module is like a spectral triple with a Fredholm operator instead of a Dirac operator, namely its a triple
		to be the abelian group of equivalence classes of Fredholm modules.
		K-theory consists of classes of vector bundles, K-homology consists of classes of Dirac operators and under the index map Dirac operators are dual to vector spaces.
	golem.ph.utexas.edu /string/archives/000627.html (2833 words)

	[No title]
		41) The stability radius of linear operator pencils,
		maximal radius of regularity of a Fredholm operator, Integral Equat.
		25) Operators with finite chain and length and the ergodic theorem
	math.univ-lille1.fr /~mbekhta/publ.html (237 words)

	AMCA: Canonical Jordan sets and Andronov-Hopf bifurcation by Boris V. Loginov
		We apply canonical Jordan sets for the construction and investigation of the branching equation (BEq) for Andronov-Hopf bifurcation of the equation
		Under group invariance conditions [2, 4] the theorem about the inheritance of group symmetry of (1) by the corresponding BEq is proved [5].
		It is considered also the case, when the operators in (1) are intertwined by discrete or parametric family of linear operators that doesn't form a group [6].
	at.yorku.ca /c/a/e/i/19.htm (336 words)

	[No title] (Site not responding. Last check: 2007-10-30)
		Formulae of Fredholm type for solutions of linear equations with generalized Fredholm operator
		On the control of linear periodic time lag systems
		The Cauchy problem for nonlinear parabolic operator equations
	journals.impan.gov.pl /cgi-bin/shvold?sm32 (174 words)

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