A new numerical method for solving the generalized regularized long wave equation is devised and analyzed. By using a reproducing kernel function, the numerical solution at each discrete time step is obtained by an ex...
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A new numerical method for solving the generalized regularized long wave equation is devised and analyzed. By using a reproducing kernel function, the numerical solution at each discrete time step is obtained by an explicit integral expression even though the scheme is truly implicit, and, hence, the computation is fully parallel. The error estimates are given and some numerical results are presented.
This paper presents a numerical method for one-dimensional Burgers' equation by the Hopf-Cole transformation and a reproducing kernel function, abbreviated as RKF. The numerical solution is given as explicit integ...
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This paper presents a numerical method for one-dimensional Burgers' equation by the Hopf-Cole transformation and a reproducing kernel function, abbreviated as RKF. The numerical solution is given as explicit integral expressions with the RKF at each time step, so that the computation is fully parallel. The stability and error estimates are derived. Numerical results for some test problems are presented and compared with the exact solutions. Some numerical results are also compared with the results obtained by other methods. The present method is easily implemented and effective. (c) 2007 Elsevier B.V. All rights reserved.
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...
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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.
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 ...
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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.
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...
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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.
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...
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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 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...
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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.
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...
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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.
A new continuous reproducingkernel interpolation function which explores the attractive features of the flexible time-frequency and space-wave number localization of a window function is developed. This method is mot...
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A new continuous reproducingkernel interpolation function which explores the attractive features of the flexible time-frequency and space-wave number localization of a window function is developed. This method is motivated by the theory of wavelets and also has the desirable attributes of the recently proposed smooth particle hydrodynamics (SPH) methods, moving least squares methods (MLSM), diffuse element methods (DEM) and element-free Galerkin methods (EFGM). The proposed method maintains the advantages of the free Lagrange or SPH methods;however, because of the addition of a correction function, it gives much more accurate results. Therefore it is called the reproducingkernel particle method (RKPM). In computer implementation RKPM is shown to be more efficient than DEM and EFGM. Moreover, if the window function is C-infinity, the solution and its derivatives are also C-infinity in the entire domain. Theoretical analysis and numerical experiments on the 1D diffusion equation reveal the stability conditions and the effect of the dilation parameter on the unusually high convergence rates of the proposed method. Two-dimensional examples of advection-diffusion equations and compressible Euler equations are also presented together with 2D multiple-scale decompositions.
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...
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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.
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