The Experts below are selected from a list of 1692 Experts worldwide ranked by ideXlab platform

S M Yaroshko - One of the best experts on this subject based on the ideXlab platform.

  • calculation of multiple characteristic numbers of a Completely Continuous Operator using the modified method of successive approximations
    Seminar Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory, 2000
    Co-Authors: S M Yaroshko
    Abstract:

    It is proved that one can calculate multiple characteristic numbers of a given Completely Continuous Operator using the modified method of successive approximations. A way to calculate the eigenfunctions of this Operator is indicated.

  • the modified iterative method for calculating Completely Continuous Operator eigenvalues and eigenfunctions
    IEEE MTT ED AP West Ukraine Chapter DIPED - 97. Direct and Inverse Problems of Electromagnetic and Acoustic Theory (IEEE Cat. No.97TH8343), 1997
    Co-Authors: S M Yaroshko
    Abstract:

    The modified iterative method (MIM) is discussed. The MIM is a method for obtaining the Completely Continuous Operator eigenvalues and eigenfunctions. The authors correct the formulation and demonstration of the MIM substantive theorem, demonstrate the MIM correlation with a moment method and give some numerical results. The ordinary successive approximation method, which is used to calculate the first eigenvalue and its eigenfunction, consists of multiple iterations by the Operator of any initial function for all vanishing next eigenfunctions in its decomposition. When the iterative process becomes stable the final result is obtained from the last two iterations. The MIM allow the use of all iterations with the initial function simultaneously to get the information about all eigenfunctions, not only about the first one. In this case there is a need for far fewer iterations to achieve a prescribed precision. It is also possible to separate each eigenfunction, even those which correspond to eigenvalues with closely placed magnitudes.

Yuji Liu - One of the best experts on this subject based on the ideXlab platform.

  • solvability of boundary value problems for singular quasi laplacian differential equations on the whole line
    Mathematical Modelling and Analysis, 2012
    Co-Authors: Yuji Liu
    Abstract:

    This paper is concerned with some integral type boundary value problems associated to second order singular differential equations with quasi-Laplacian on the whole line. The emphasis is put on the one-dimensional p-Laplacian term involving a nonnegative function ρ that may be singular at t = 0 and such that . A Banach space and a nonlinear Completely Continuous Operator are defined in this paper. By using the Schauder's fixed point theorem, sufficient conditions to guarantee the existence of at least one solution are established. An example is presented to illustrate the main theorem.

Mutlu Gökhan - One of the best experts on this subject based on the ideXlab platform.

  • Associated functions of non-selfadjoint Sturm-Liouville Operator with Operator coefficient
    Işık University Press, 2021
    Co-Authors: Mutlu Gökhan
    Abstract:

    Sturm-Liouville Operator equation with selfadjoint Operator coefficent has been studied in detail. In this paper, we consider the Sturm-Liouville Operator equation with non-selfadjoint Operator coefficent. Namely, we examine the non-selfadjoint SturmLiouville Operator L which is generated in L2(R+, H) by the differential expression L(Y ) = −Y’’ + Q(x)Y, 0 < x < ∞, with Operator coefficient together with the boundary condition Y (0) = 0, where Q(x) is a non-selfadjoint, Completely Continuous Operator in a separable Hilbert space H for each x ∈ (0, ∞). We find the associated functions corresponding to the eigenvalues and spectral singularities of L. Moreover, we prove that the associated functions corresponding to the eigenvalues belong to L2 (R+, H) while the associated functions corresponding to the spectral singularities do not.Publisher's Versio

G Mutlu - One of the best experts on this subject based on the ideXlab platform.

  • spectral properties of non selfadjoint sturm liouville Operator with Operator coefficient
    Journal of Mathematical Analysis and Applications, 2017
    Co-Authors: Elgiz Bairamov, E K Arpat, G Mutlu
    Abstract:

    Abstract In this paper, we consider the Sturm–Liouville Operator L generated in L 2 ( R + , H ) by the differential expression L ( Y ) = − Y ″ + Q ( x ) Y , 0 x ∞ , with the boundary condition Y ( 0 ) = 0 , where Q ( x ) is a non-selfadjoint, Completely Continuous Operator in H for every x > 0 . Here H is a separable Hilbert space, B ( H ) denotes the space of bounded Operators in H and L 2 ( R + , H ) denotes the space of square-integrable, strongly-measurable vector-valued functions defined on ( 0 , ∞ ) . In particular, we find some special solutions of the equation L ( Y ) = λ 2 Y including Jost solution, then investigate the point spectrum of L under certain conditions on Q ( x ) . We obtain the resolvent of L , if Q ( x ) is quasi-selfadjoint i.e. there exists P ∈ B ( H ) such that P − 1 ∈ B ( H ) , P is positive and Q ⁎ ( x ) = P Q ( x ) P − 1 for every x > 0 . We also show that L has a finite number of spectral singularities.

Zhen Chen - One of the best experts on this subject based on the ideXlab platform.

  • the order preserving convergence for spectral approximation of self adjoint Completely Continuous Operators
    Science China-mathematics, 2008
    Co-Authors: Yidu Yang, Zhen Chen
    Abstract:

    This paper discusses the order-preserving convergence for spectral approximation of the self-adjoint Completely Continuous Operator T. Under the condition that the approximate Operator Th converges to T in norm, it is proven that the k-th eigenvalue of Th converges to the k-th eigenvalue of T. (We sorted the positive eigenvalues in decreasing order and negative eigenvalues in increasing order.) Then we apply this result to conforming elements, nonconforming elements and mixed elements of self-adjoint elliptic differential Operators eigenvalue problems, and prove that the k-th approximate eigenvalue obtained by these methods converges to the k-th exact eigenvalue.