• Communications of the Korean Mathematical Society
• /
• v.9 no.3
• /
• pp.593-598
• /
• 1994

In this note we give some results on the jump (due to Kato [5] and West [7]) of a semi-Fredholm operator. Throughout this note, suppose X is an Banach space and write L(X) for the set of all bounded linear operators on X. A operator $T \in L(x)$ is called upper semi-Fredholm if it has closed range with finite dimensional null space, and lower semi-Fredholm if it has closed range with its range of finite co-dimension. It T is either upper or lower semi-Fredholm we shall call it semi-Fredholm and Fredholm it is both. The index of a (semi-) Fredholm operator T is given by $$ index(T) = n(T) = d(T),$$ where $n(T) = dim T^{-1}(0)$ and d(T) = codim T(X).

• Korean Journal of Mathematics
• /
• v.4 no.1
• /
• pp.71-76
• /
• 1996

The purpose of the present paper is to derive the perturbations and jumps of semi-Fredholm operators.

• Communications of the Korean Mathematical Society
• /
• v.10 no.2
• /
• pp.331-335
• /
• 1995

We prover Fredholm alternatives for AF algebras: If an element have the finite null projection and the confinite range projection then its image in the relative Calkin algebra is invertible.

• The Transactions of the Korean Institute of Electrical Engineers D
• /
• v.53 no.4
• /
• pp.207-211
• /
• 2004

We consider a class of uncertain nonlinear systems containing the uncertainties without a priori information except that they are bounded. For such systems, we assume that the upper bound of the uncertainties is represented as a Fredholm integral equation of the first kind and we propose an adaptation law that is capable of estimating the upper bound. Using this adaptive upper bound, a continuous robust control which renders uncertain nonlinear systems uniformly ultimately bounded is designed.

• Journal of applied mathematics & informatics
• /
• v.6 no.1
• /
• pp.163-174
• /
• 1999

The purpose of this paper is to obtain the solution of Fredholm-Volterra integral equation with singular kernel in the space $L_2(-1, 1)\times C(0,T), 0 \leq t \leq T< \infty$, under certain conditions,. The numerical method is used to solve the Fredholm integral equation of the second kind with weak singular kernel using the Toeplitz matrices. Also the error estimate is computed and some numerical examples are computed using the MathCad package.

• Korean Journal of Mathematics
• /
• v.25 no.3
• /
• pp.323-334
• /
• 2017

In this paper, we propose a combined form for solving nonlinear interval Volterra-Fredholm integral equations of the second kind based on the modifying Laplace Adomian decomposition method. We find the exact solutions of nonlinear interval Volterra-Fredholm integral equations with less computation as compared with standard decomposition method. Finally, an illustrative example has been solved to show the efficiency of the proposed method.

• Kyungpook Mathematical Journal
• /
• v.45 no.4
• /
• pp.471-480
• /
• 2005

This paper deals with some useful methods of solving the one-dimensional integral equation of Fredholm type. Application of the reduction techniques with a view to inverting a class of integral equation with Lauricella function in the kernel, Riemann-Liouville fractional integral operators as well as Weyl operators have been made to reduce to this class to generalized Stieltjes transform and inversion of which yields solution of the integral equation. Use of Mellin transform technique has also been made to solve the Fredholm integral equation pertaining to certain polynomials and H-functions.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.3
• /
• pp.1021-1027
• /
• 2013

We consider right and left Fredholm operator matrices of the form $\[\array{A&C\\T&S}\]$, which are linear and bounded on the Banach space $Z=X{\oplus}Y$.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.2
• /
• pp.509-520
• /
• 2020

We study the Toeplitz operators on the holomorphic and pluriharmonic Dirichlet spaces of the polydisk in terms of when Toeplitz operator is Fredholm operator there. Consequently, we describe the essential spectrum of Toeplitz operators.

• Honam Mathematical Journal
• /
• v.39 no.2
• /
• pp.175-185
• /
• 2017

In this paper we consider Toeplitz operators on the pluriharmonic Dirichlet space of the unit ball in the n-dimensional complex space. We then characterize Fredholm Toeplitz operators and describe the essential spectrum of a Toeplitz operator as a consequence.