In this paper, a new numerical algorithm is provided to solve nonlinear three-point boundary value problems in a very favorable reproducingkernel space which satisfies all boundary conditions. Its reproducingkernel ...
详细信息
In this paper, a new numerical algorithm is provided to solve nonlinear three-point boundary value problems in a very favorable reproducingkernel space which satisfies all boundary conditions. Its reproducing kernel function is discussed in detail. We also prove that the approximate solution and its first and second order derivatives all converge uniformly. The numerical experiments show that the algorithm is quite accurate and efficient for solving nonlinear second order three-point boundary value problems. (C) 2012 Elsevier Inc. All rights reserved.
Conventional kernel support vector machine (KSVM) has the problem of slow training speed, and single kernel extreme learning machine (KELM) also has some performance limitations, for which this paper proposes a new co...
详细信息
Conventional kernel support vector machine (KSVM) has the problem of slow training speed, and single kernel extreme learning machine (KELM) also has some performance limitations, for which this paper proposes a new combined KELM model that build by the polynomial kernel and reproducingkernel on Sobolev Hilbert space. This model combines the advantages of global and local kernelfunction and has fast training speed. At the same time, an efficient optimization algorithm called cuckoo search algorithm is adopted to avoid blindness and inaccuracy in parameter selection. Experiments were performed on bi-spiral benchmark dataset, Banana dataset, as well as a number of classification and regression datasets from the UCI benchmark repository illustrate the feasibility of the proposed model. It achieves the better robustness and generalization performance when compared to other conventional KELM and KSVM, which demonstrates its effectiveness and usefulness.
We introduce new functional spaces generalizing the weighted Bergman and Dirichlet spaces on the complex disk as well as the Bargmann-Fock spaces on the whole complex plane . We give a complete description of the cons...
详细信息
We introduce new functional spaces generalizing the weighted Bergman and Dirichlet spaces on the complex disk as well as the Bargmann-Fock spaces on the whole complex plane . We give a complete description of the considered spaces. Mainly, we are interested in giving explicit formulas for their reproducing kernel functions and their asymptotic behavior as R goes to infinity.
We consider a class of bounded linear operators on Hilbert space called n-hypercontractions which relates naturally to adjoint shift operators on certain vector-valued standard weighted Bergman spaces on the unit disc...
详细信息
We consider a class of bounded linear operators on Hilbert space called n-hypercontractions which relates naturally to adjoint shift operators on certain vector-valued standard weighted Bergman spaces on the unit disc. In the context of n-hypercontractions in the class C-0. we introduce a counterpart to the so-called characteristic operator function for a contraction operator. This generalized characteristic operator function W-n,W-T is an operator-valued analytic function in the unit disc whose values are operators between two Hilbert spaces of defect type. Using an operator-valued function of the form W-n,W-T, we parametrize the wandering subspace for a general shift invariant subspace of the corresponding vector-valued standard weighted Bergman space. The operator-valued analytic function W-n,W-T is shown to act as a contractive multiplier from the Hardy space into the associated standard weighted Bergman space. (c) 2006 Elsevier Inc. All rights reserved.
In this paper we construct a large class of multiplication operators on reproducingkernel Hilbert spaces which are homogeneous with respect to the action of the Mobius group consisting of bi-holomorphic automorphisms...
详细信息
In this paper we construct a large class of multiplication operators on reproducingkernel Hilbert spaces which are homogeneous with respect to the action of the Mobius group consisting of bi-holomorphic automorphisms of the unit disc D. Indeed, this class consists of exactly those operators for which the associated unitary representation of the universal covering group of the Mobius group is multiplicity free. For every m is an element of N we have a family of operators depending on m + 1 positive real parameters. The kernelfunction is calculated explicitly. It is proved that each of these operators is bounded, lies in the Cowen-Douglas class of D and is irreducible. These operators are shown to be mutually pairwise unitarily inequivalent. (C) 2008 Elsevier Inc. All rights reserved.
Certain Hilbert spaces of polynomials, called Szego spaces [II], are studied. A transformation, called Hilbert transformation, is constructed for every polynomial associated with a Szego space. An orthogonal set is fo...
详细信息
Certain Hilbert spaces of polynomials, called Szego spaces [II], are studied. A transformation, called Hilbert transformation, is constructed for every polynomial associated with a Szego space. An orthogonal set is found in a Szego space which determines the norm of the space. A matrix factorization theory is obtained for defining polynomials. Measures associated with a Szego space are parametrized by functions which are analytic and bounded by one in the unit disk. A fundamental factorization theorem relates Szego spaces to weighted Hardy spaces.
Abstract: We study the operators $\Delta (X) = \sum \nolimits _1^n {{M_n}X{N_n}}$ and ${\Delta ^{\ast }}(X) = \sum \nolimits _1^n {M_n^{\ast }XN_n^{\ast }}$ which map the algebra of all bounded linear operator...
详细信息
Abstract: We study the operators $\Delta (X) = \sum \nolimits _1^n {{M_n}X{N_n}}$ and ${\Delta ^{\ast }}(X) = \sum \nolimits _1^n {M_n^{\ast }XN_n^{\ast }}$ which map the algebra of all bounded linear operators on a separable Hubert space to itself, where $\langle {M_n}\rangle _1^m$ and $\langle {N_n}\rangle _1^m$ are separately commuting sequences of normal operators. We prove that (1) when $m \leqslant 2$, the Hilbert-Schmidt norms of $\Delta (X)$ and ${\Delta ^{\ast }}(X)$ are equal (finite or infinite); (2) for $m \geqslant 3$, if $\Delta (X)$ and ${\Delta ^{\ast }}(X)$ are Hilbert-Schmidt operators, then their Hilbert-Schmidt norms are equal; (3) if $\Delta ,{\Delta ^{\ast }}$ have the property that for each $X,\Delta (X) = 0$ implies ${\Delta ^{\ast }}(X) = 0$, then for each $X$, if $\Delta (X)$ is a Hilbert-Schmidt operator then ${\Delta ^{\ast }}^2(X)$ is also and the latter has the same Hilbert-Schmidt norm as ${\Delta ^2}(X)$. Note that Fuglede’s Theorem is immediate from $(1)$ in the case $m = 2,{M_1} = {N_2}$ and ${N_1} = I = - {M_2}$. The proofs employ the duality between the trace class and the class of all bounded linear operators and, unlike the early proofs of Fuglede’s Theorem, they are free of complex function theory.
By a theorem of G.-C. Rota, every (linear) operator T on a Hilbert space with spectral radius less than one is similar to the adjoint of the unilateral shift S of infinite multiplicity restricted to an invariant subsp...
详细信息
By a theorem of G.-C. Rota, every (linear) operator T on a Hilbert space with spectral radius less than one is similar to the adjoint of the unilateral shift S of infinite multiplicity restricted to an invariant subspace. This theorem is shown to be true in a rather general context, where S is multiplication by z on a Hilbert space of functions analytic on an open subset D of the complex plane, and T is an operator with spectrum contained in D. A several-variable version for an N-tuple of commuting operators with a corollary concerning complete spectral sets is also presented.
In this paper we study orthogonal polynomials with asymptotically periodic reflection coefficients. It's known that the support of the orthogonality measure of such polynomials consists of several arcs. We are mai...
详细信息
In this paper we study orthogonal polynomials with asymptotically periodic reflection coefficients. It's known that the support of the orthogonality measure of such polynomials consists of several arcs. We are mainly interested in the asymptotic behaviour on the support and derive weak convergence results: fur the orthogonal polynomials and also for the Christoffel function. (C) 2000 Academic Press.
Meyer wavelet is a classic wavelet, it has many good properties. For example derivation infinitely, smoothness, attenuates fast and its spectrum is finite, Meyer wavelet is beneficial to numerical calculate, so it app...
详细信息
ISBN:
(纸本)9781479913909
Meyer wavelet is a classic wavelet, it has many good properties. For example derivation infinitely, smoothness, attenuates fast and its spectrum is finite, Meyer wavelet is beneficial to numerical calculate, so it applies widely in engineering majors. In this paper, we can discuss the properties of the image space of classic Meyer wavelet transform. According to the properties of reproducingkernel, In this space, we obtain the reproducing kernel function two expressions When scale factor is fixed. We also use the additive operation and norm operation of reproducingkernel space to describe the Meyer image space. This article provides one method about study the image space of the class of Meyer wavelets transform. In signal processing field, which is beneficial to choose wavelet base well. And in the actual application of the class of Meyer wavelet, by the results of this paper, in which can help us to choose a more suitable Meyer wavelet. We can give the optimal algorithm, programming by computer and develop the application software.
暂无评论