Basic properties of unbounded weighted conditional type operators

In this paper we consider unbounded weighted conditional type (WCT) operators on Lp-space. We provide some conditions under which WCT operators on Lp-spaces are densely defined. Specifically, we obtain a dense subset of their domain. Moreover, we get that a WCT operator is continuous if and only if it is every where defined. A description of polar decomposition, spectrum, spectral radius, normality and hyponormality of WCT operators in this context are provided. Finally, we apply some results of hyperexpansive operators to WCT operators on the Hilbert space L2(?). As a consequence hyperexpansive multiplication operators are investigated.

Biharmonic heat equation with gradient non-linearity on Lp space

In this paper, we deal with the biharmonic heat equation with gradient non-linearity. Under the suitable condition of the initial datum, we show that the global unique existence of the mild solution. The main technique in the paper is to use Banach?s fixed point theorem in combination with the Lp-Lq evaluation of biharmonic operator.

On basicity of the degenerate trigonometric system with excess

The basis properties (completeness, minimality and Schauder basicity) of systems of the form {ω(t)φn(t)}, where {φn(t)} is an exponential or trigonometric (cosine or sine) systems, have been investigated in several papers. Concrete examples of the weight function ω(t) are known for which the system itself is not complete and minimal but has excess – becomes complete and minimal in corresponding Lp space only after elimination of some of its elements. The aim of this paper is to show that if ω(t) is any measurable weight function such that the system {ω(t) sin nt}n∊ℕ has excess, then neither this system itself, nor a system obtained from it by elimination of an element, is not a Schauder basis.

On properties of multiplication conditional type operators between Lp-space

In this paper, firstwe give some necessary and sufficient conditions for multiplication conditional type operators between two Lp-spaces to have closed range. Then we investigate Fredholm ones when the underlying measure space is non-atomic. Finally we give some examples.