Equiconvergence theorems for differential operators

Bernstein Equiconvergence and Fej Er Type Theorems for General Rational Fourier Series Bernstein Equiconvergence and Fej Er Type Theorems for General Rational Fourier Series

Let w() be a positive weight function on the interval ;) and associate the positive deenite inner product on the unit circle of the complex plane by hf; gi w = 1 2 R f(e ii)g(e ii)w()d. For a sequence of points f k g 1 k=1 included in a compact subset of the open unit disk, we consider the orthogonal rational functions (ORF) f k g 1 k=0 that are obtained by orthogonalization of the sequence f1;...

properties of M−hyoellipticity for pseudo differential operators

In this paper we study properties of symbols such that these belong to class of symbols sitting insideSm ρ,φ that we shall introduce as the following. So for because hypoelliptic pseudodifferential operatorsplays a key role in quantum mechanics we will investigate some properties of M−hypoelliptic pseudodifferential operators for which define base on this class of symbols. Also we consider maxi...

Saturation theorems for diseretized linear operators

There is a well developed theory of saturation for positive convolution operators on C*, the space of 2n-periodic and continuous functions. Up until recently, this was suitable to handle almost all the important approximation processes on C*. Now, however, some new and interesting sequences of operators have been obtained for C* by discretizing convolution operators [1], [5]. Such a discretized...

Fixed point theorems for sums of operators

Spectral Mapping Theorems for Hyponormal Operators

Let T=H+iK be hyponormal and Q be a strictly monotone increasing continuous function on s(H ). We define ~ Q(T ) by ~ Q(T )=Q(H )+iK. In this paper, we show that if z is an isolated eigenvalue of ~ Q(T ), then the corresponding Riesz projection is self-adjoint. Also we introduce Xia spectrum and study the existence of an invariant subspace of an operator ~ Q(T ).