We analyze the spectrum of a certain singular integral operator on the space (L2(fi))3 where fi is contained in three dimensional Euclidean space and has a Lipschitz continuous boundary. This operator arises in the integral formulation of the magnetostatic field problem. We decompose (L2(fi))3 into invariant subspaces: in one where the operator is the zero map; in one, the identity map; and in ...

properties of the hybrid of block-pulse functions and lagrange polynomials based on the legendre-gauss-type points are investigated and utilized to define the composite interpolation operator as an extension of the well-known legendre interpolation operator. the uniqueness and interpolating properties are discussed and the corresponding differentiation matrix is also introduced. the applicabili...

let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . in this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . as an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via the linear operator .

An index theory for uniformly locally finite (ULF) graphs is developed based on the adjacency operator A acting on the space of bounded sequences defined on the vertices. It turns out that the characterization by upper and lower nonnegative eigenvectors is an appropriate tool to overcome the difficulties imposed by the `∞–setting. A distinctive property of the spectral radius r∞(A) in `∞ is the...

Let T and S be two bounded linear operators from Banach spaces X into Y and suppose that T is Fredholm and the stability number k(T ;S) is 0. Let d(T ;S) be the supremum of all r > 0 such that dimN(T − λS) and codim R(T − λS) are constant for all λ with |λ| < r. It was proved in 1980 by H. Bart and D.C. Lay that d(T ;S) = limn→∞ γn(T ;S) , where γn(T ;S) are some non-negative (extended) real nu...