Search results for "functions"

showing 10 items of 1066 documents

Norm, essential norm and weak compactness of weighted composition operators between dual Banach spaces of analytic functions

2017

Abstract In this paper we estimate the norm and the essential norm of weighted composition operators from a large class of – non-necessarily reflexive – Banach spaces of analytic functions on the open unit disk into weighted type Banach spaces of analytic functions and Bloch type spaces. We also show the equivalence of compactness and weak compactness of weighted composition operators from these weighted type spaces into a class of Banach spaces of analytic functions, that includes a large family of conformally invariant spaces like BMOA and analytic Besov spaces.

Discrete mathematicsMathematics::Functional AnalysisApplied MathematicsTopological tensor product010102 general mathematicsEberlein–Šmulian theoremWeakly compact operatorBloch type spaceBanach manifoldFinite-rank operator01 natural sciences010101 applied mathematicsEssential normWeighted spaces of analytic functionsFréchet spaceWeighted composition operatorInterpolation spaceBirnbaum–Orlicz space0101 mathematicsLp spaceAnalysisMathematics
researchProduct

A Riemann manifold structure of the spectra of weighted algebras of holomorphic functions

2009

[EN] In this paper we give general conditions on a countable family V of weights on an unbounded open set U in a complex Banach space X such that the weighted space HV (U) of holomorphic functions on U has a Frechet algebra structure. For such weights it is shown that the spectrum of HV(U) has a natural analytic manifold structure when X is a symmetrically regular Banach space, and in particular when X = C-n. (C) 2009 Elsevier Ltd. All rights reserved.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsFréchet algebraWeighted space of holomorphic functionsHolomorphic functional calculusInfinite-dimensional vector functionSpectrum (functional analysis)Holomorphic functionFrechet algebraBanach manifoldAnalytic manifold structureAnalytic manifoldBergman spaceSymmetrically regular Banach spaceGeometry and TopologyMATEMATICA APLICADAWeighted spaceMathematicsTopology
researchProduct

A space of projections on the Bergman space

2010

We define a set of projections on the Bergman space A 2 , which is parameterized by an ane subset of a Banach space of holomorphic functions in the disk and which includes the classical Forelli-Rudin projections.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsMathematics::Complex VariablesGeneral MathematicsInfinite-dimensional vector functionHolomorphic functionBanach spaceMathematics::General TopologyQuotient space (linear algebra)Continuous functions on a compact Hausdorff spaceBergman spaceBesov spaceBergman kernelMathematicsAnnales Academiae Scientiarum Fennicae Mathematica
researchProduct

2-SYMMETRIC CRITICAL POINT THEOREMS FOR NON-DIFFERENTIABLE FUNCTIONS

2008

AbstractIn this paper, some min–max theorems for even andC1functionals established by Ghoussoub are extended to the case of functionals that are the sum of a locally Lipschitz continuous, even term and a convex, proper, lower semi-continuous, even function. A class of non-smooth functionals admitting an unbounded sequence of critical values is also pointed out.

Discrete mathematicsNon-smooth critical point theory minmax theorems symmetric functionsGeneral MathematicsRegular polygonEven and odd functionsDifferentiable functionLipschitz continuityCritical point (mathematics)MathematicsGlasgow Mathematical Journal
researchProduct

General inductive inference types based on linearly-ordered sets

1996

In this paper, we reconsider the definitions of procrastinating learning machines. In the original definition of Freivalds and Smith [FS93], constructive ordinals are used to bound mindchanges. We investigate the possibility of using arbitrary linearly ordered sets to bound mindchanges in a similar way. It turns out that using certain ordered sets it is possible to define inductive inference types more general than the previously known ones. We investigate properties of the new inductive inference types and compare them to other types.

Discrete mathematicsOrdered setRecursive functionsInductive reasoningConstructiveMaximal elementMathematics
researchProduct

The convolution operation on the spectra of algebras of symmetric analytic functions

2012

Abstract We show that the spectrum of the algebra of bounded symmetric analytic functions on l p , 1 ≤ p + ∞ with the symmetric convolution operation is a commutative semigroup with the cancellation law for which we discuss the existence of inverses. For p = 1 , a representation of the spectrum in terms of entire functions of exponential type is obtained which allows us to determine the invertible elements.

Discrete mathematicsPower sum symmetric polynomialTriple systemSpectra of algebrasApplied MathematicsSymmetric polynomialsStanley symmetric functionComplete homogeneous symmetric polynomialSymmetric convolutionSymmetric functionEntire functions of exponential typeElementary symmetric polynomialRing of symmetric functionsPolynomials and analytic functions on Banach spacesAnalysisMathematicsJournal of Mathematical Analysis and Applications
researchProduct

Linearization of holomorphic mappings on fully nuclear spaces with a basis

1994

In [13] Mazet proved the following result.If U is an open subset of a locally convex space E then there exists a complete locally convex space (U) and a holomorphic mapping δU: U→(U) such that for any complete locally convex space F and any f ɛ ℋ (U;F), the space of holomorphic mappings from U to F, there exists a unique linear mapping Tf: (U)→F such that the following diagram commutes;The space (U) is unique up to a linear topological isomorphism. Previously, similar but less general constructions, have been considered by Ryan [16] and Schottenloher [17].

Discrete mathematicsPure mathematicsLinearizationGeneral MathematicsSuperfunctionHolomorphic functional calculusComputingMethodologies_DOCUMENTANDTEXTPROCESSINGHolomorphic functionAnalyticity of holomorphic functionsOpen mapping theorem (complex analysis)Identity theoremMathematicsGlasgow Mathematical Journal
researchProduct

Geometric Properties of Planar BV -Extension Domains

2009

We investigate geometric properties of those planar domains that are extension for functions with bounded variation.We start from a characterization of such domains given by Burago–Maz'ya and prove that a bounded, simply connected domain is a BV -extension domain if and only if its com- plement is quasiconvex. We further prove that the extension property is a bi-Lipschitz invariant and give applications to Sobolev extension domains.

Discrete mathematicsQuasiconformal mappingMathematics::Analysis of PDEsGeometric propertySobolev spaceQuasiconvex functionExtension domains; Sobolev spaces; Functions with bounded variationPlanarSobolev spacesFunctions with bounded variationBounded functionSimply connected spaceInvariant (mathematics)Extension domainsMathematics
researchProduct

Learning with confidence

1996

Herein we investigate learning in the limit where confidence in the current conjecture accrues with time. Confidence levels are given by rational numbers between 0 and 1. The traditional requirement that for learning in the limit is that a device must converge (in the limit) to a correct answer. We further demand that the associated confidence in the answer (monotonically) approach 1 in the limit. In addition to being a more realistic model of learning, our new notion turns out to be a more powerful as well. In addition, we give precise characterizations of the classes of functions that are learnable in our new model(s).

Discrete mathematicsRational numberConjectureCurrent (mathematics)Recursive functionsMonotonic functionLimit (mathematics)Inductive reasoningMathematics
researchProduct

Enumeration of L-convex polyominoes by rows and columns

2005

In this paper, we consider the class of L-convex polyominoes, i.e. the convex polyominoes in which any two cells can be connected by a path of cells in the polyomino that switches direction between the vertical and the horizontal at most once.Using the ECO method, we prove that the number fn of L-convex polyominoes with perimeter 2(n + 2) satisfies the rational recurrence relation fn = 4fn-1 - 2fn-2, with f0 = 1, f1 = 2, f2 = 7. Moreover, we give a combinatorial interpretation of this statement. In the last section, we present some open problems.

Discrete mathematicsRecurrence relationECO methodGeneral Computer SciencePolyominoGenerating functionRegular polygonRow and column spacesTheoretical Computer ScienceInterpretation (model theory)Generating functionsCombinatoricsSection (fiber bundle)Path (graph theory)Convex polyominoesComputer Science(all)MathematicsTheoretical Computer Science
researchProduct