We consider abstract operator equations Fu = y, where F is a compact linear operator between Hilbert spaces U and V , which are function spaces on closed, finite dimensional Riemannian manifolds, respectively. This setting is of interest in numerous applications such as Computer Vision and non-destructive evaluation. In this work, we study the approximation of the solution of the ill-posed oper...

We study the global hypoellipticity problem for certain linear operators in Komatsu classes of Roumieu and Beurling type on compact manifolds. present an approach by combining a characterization these spaces via eigenfuction expansions, generated elliptic operator, analysis matrix-symbols obtained expansions.

We prove that a normal operator on a separable Hubert space can be written as a diagonal operator plus a compact operator. If, in addition, the spectrum lies in a rectifiable curve we show that the compact operator can be made HilbertSchmidt. In 1909 Hermann Weyl proved [3] that each bounded Hermitian operator on a separable Hubert space can be written as the sum of a diagonal operator and a co...

We consider the eigenvalue problem of certain kind of non-compact linear operators given as the sum of a multiplication and a kernel operator. A degenerate kernel method with piecewise linear interpolation with respect to the second variable is used to approximate eigenvalues. It is shown that the error is of order O(h). A bound for the condition number of this method is obtained. By a numerica...

In this paper, we consider the optimal disturbance rejection problem for (possibly infinite dimensional) linear time-varying (LTV) systems using a framework based on operator algebras of classes of bounded linear operators. After reducing the problem to a shortest distance minimization in a space of bounded linear operators, duality theory is applied to show existence of optimal solutions, whic...

It has been recently shown that ||Fn(A)|| ≤ 2, where A is a linear continuous operator acting in a Hilbert space, and Fn is the Faber polynomial of degree n corresponding to some convex compact E ⊂ C containing the numerical range of A. Such an inequality is useful in numerical linear algebra, it allows for instance to derive error bounds for Krylov subspace methods. In the present paper we ext...

An analytic self-map φ : D → D of the open unit disk D in the complex plane induces the composition operator Cφ on H(D), the space of holomorphic functions on D, defined by Cφ(f) = f ◦φ. A basic goal in the study of composition operators is to relate function theoretic properties of φ to operator theoretic properties of Cφ. Here we review some results that characterize when φ induces a bounded ...