scholarly journals Fine Spectra of Tridiagonal Symmetric Matrices

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Muhammed Altun
Keyword(s):  
Explicit Form ◽  
Resolvent Operator ◽  
Sequence Spaces ◽  
Symmetric Matrices ◽  
Infinite Matrices ◽  
Banded Matrices ◽  
Lower Triangular ◽  
The Resolvent Operator

The fine spectra of upper and lower triangular banded matrices were examined by several authors. Here we determine the fine spectra of tridiagonal symmetric infinite matrices and also give the explicit form of the resolvent operator for the sequence spaces , , , and .

The Resolvent Operator

2017 ◽  
Author(s):  
Charles L. Epstein ◽  
Rafe Mazzeo
Keyword(s):  
Cauchy Problem ◽  
Heat Equation ◽  
Laplace Transform ◽  
Heat Kernel ◽  
Resolvent Operator ◽  
Contour Integration ◽  
Resolvent Kernel ◽  
The Laplace Transform ◽  
Elliptic Estimates ◽  
The Resolvent Operator

This chapter describes the construction of a resolvent operator using the Laplace transform of a parametrix for the heat kernel and a perturbative argument. In the equation (μ‎-L) R(μ‎) f = f, R(μ‎) is a right inverse for (μ‎-L). In Hölder spaces, these are the natural elliptic estimates for generalized Kimura diffusions. The chapter first constructs the resolvent kernel using an induction over the maximal codimension of bP, and proves various estimates on it, along with corresponding estimates for the solution operator for the homogeneous Cauchy problem. It then considers holomorphic semi-groups and uses contour integration to construct the solution to the heat equation, concluding with a discussion of Kimura diffusions where all coefficients have the same leading homogeneity.

Controllability for some nonlinear impulsive partial functional integrodifferential systems with infinite delay in Banach spaces

2020 ◽  
Vol 4 (2) ◽  
pp. 104-115
Author(s):  
Khalil Ezzinbi ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Resolvent Operator ◽  
Measure Of Noncompactness ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Mönch Fixed Point Theorem ◽  
The Resolvent Operator

This work concerns the study of the controllability for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces. We give sufficient conditions that ensure the controllability of the system by supposing that its undelayed part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point Theorem. As a result, we obtain a generalization of the work of K. Balachandran and R. Sakthivel (Journal of Mathematical Analysis and Applications, 255, 447-457, (2001)) and a host of important results in the literature, without assuming the compactness of the resolvent operator. An example is given for illustration.

scholarly journals Inversion of Bilateral Basic Hypergeometric Series

10.37236/1703 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Michael Schlosser
Keyword(s):  
Hypergeometric Series ◽  
Basic Hypergeometric Series ◽  
Matrix Inversion ◽  
Infinite Matrices ◽  
Inversion Result ◽  
Matrix Inverse ◽  
Bilateral Basic Hypergeometric Series ◽  
Summation Theorem ◽  
Lower Triangular

We present a new matrix inverse with applications in the theory of bilateral basic hypergeometric series. Our matrix inversion result is directly extracted from an instance of Bailey's very-well-poised ${}_6\psi_6$ summation theorem, and involves two infinite matrices which are not lower-triangular. We combine our bilateral matrix inverse with known basic hypergeometric summation theorems to derive, via inverse relations, several new identities for bilateral basic hypergeometric series.

scholarly journals The αAB-, βAB-, γab- and NAB-duals for sequence spaces

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6219-6231
Author(s):  
D. Foroutannia ◽  
H. Roopaei
Keyword(s):  
Sequence Spaces ◽  
The Other ◽  
Infinite Matrices ◽  
Multiplier Space

Let A = (an,k) and B = (bn,k) be two infinite matrices with real entries. The main purpose of this paper is to generalize the multiplier space for introducing the concepts of ?AB-, ?AB-, ?AB-duals and NAB-duals. Moreover, these duals are investigated for the sequence spaces X and X(A), where X ? {c0, c, lp} for 1 ? p ? ?. The other purpose of the present study is to introduce the sequence spaces X(A,?) = {x=(xk): (?x?k=1 an,kXk - ?x?k=1 an-1,kXk)? n=1 ? X}, where X ? {l1,c,c0}, and computing the NAB-(or Null) duals and ?AB-duals for these spaces.

scholarly journals On zeta functions associated to symmetric matrices III – An explicit form of L-Functions

1997 ◽  
Vol 146 ◽  
pp. 149-183 ◽  
Author(s):  
Tomoyoshi Ibukiyama ◽  
Hiroshi Saito
Keyword(s):  
Explicit Form ◽  
Zeta Functions ◽  
Symmetric Matrices ◽  
Special Values

Abstract.In [I-S2], we gave an explicit form of zeta functions associated to the space of symmetric matrices. In this paper, the case of L-functions is treated. In the case of definite symmetric matrices, we show the ratinality of special values of these L-functions.

scholarly journals Approximation solvability for a system of implicit nonlinear variational inclusions with Η-monotone operators

2018 ◽  
Vol 51 (1) ◽  
pp. 241-254
Author(s):  
Jong Kyu Kim ◽  
Muhammad Iqbal Bhat
Keyword(s):  
Iterative Algorithm ◽  
Resolvent Operator ◽  
Monotone Operators ◽  
Inner Product ◽  
Operator Technique ◽  
Variational Inclusions ◽  
Inclusion Problems ◽  
Resolvent Operator Technique ◽  
The Resolvent Operator ◽  
New System

AbstractIn this paper, we introduce and study a new system of variational inclusions which is called a system of nonlinear implicit variational inclusion problems with A-monotone and H-monotone operators in semi-inner product spaces. We define the resolvent operator associated with A-monotone and H-monotone operators and prove its Lipschitz continuity. Using resolvent operator technique, we prove the existence and uniqueness of solution for this new system of variational inclusions. Moreover, we suggest an iterative algorithm for approximating the solution of this system and discuss the convergence analysis of the sequences generated by the iterative algorithm under some suitable conditions.

scholarly journals On Mixed Equilibrium Problems in Hadamard Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Chinedu Izuchukwu ◽  
Kazeem Olalekan Aremu ◽  
Olawale Kazeem Oyewole ◽  
Oluwatosin Temitope Mewomo ◽  
Safeer Hussain Khan
Keyword(s):  
Equilibrium Problem ◽  
Resolvent Operator ◽  
Equilibrium Problems ◽  
Existence Of Solution ◽  
Mixed Equilibrium Problem ◽  
Proximal Point ◽  
Unique Existence ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium ◽  
The Resolvent Operator

The main purpose of this paper is to study mixed equilibrium problems in Hadamard spaces. First, we establish the existence of solution of the mixed equilibrium problem and the unique existence of the resolvent operator for the problem. We then prove a strong convergence of the resolvent and a Δ-convergence of the proximal point algorithm to a solution of the mixed equilibrium problem under some suitable conditions. Furthermore, we study the asymptotic behavior of the sequence generated by a Halpern-type PPA. Finally, we give a numerical example in a nonlinear space setting to illustrate the applicability of our results. Our results extend and unify some related results in the literature.

scholarly journals Generalized Implicit Set-Valued Variational Inclusion Problem with ⊕ Operation

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 421
Author(s):  
Rais Ahmad ◽  
Imran Ali ◽  
Saddam Husain ◽  
A. Latif ◽  
Ching-Feng Wen
Keyword(s):  
Resolvent Operator ◽  
Convergence Result ◽  
Variational Inclusion ◽  
Inclusion Problem ◽  
Variational Inclusion Problem ◽  
Special Cases ◽  
The Resolvent Operator

In this paper, we consider a resolvent operator which depends on the composition of two mappings with ⊕ operation. We prove some of the properties of the resolvent operator, that is, that it is single-valued as well as Lipschitz-type-continuous. An existence and convergence result is proven for a generalized implicit set-valued variational inclusion problem with ⊕ operation. Some special cases of a generalized implicit set-valued variational inclusion problem with ⊕ operation are discussed. An example is constructed to illustrate some of the concepts used in this paper.

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