Sets of weak sequential continuity for polynomials
Abstract Let P : E → K be an N-homogeneous polynomial, where E is a Banach space over K = R or C . We study properties of the set Cp = {x ∈ E : P is weakly sequentially continuous at x}.
Homomorphisms between Algebras of Holomorphic Functions
For two complex Banach spaces and , in this paper, we study the generalized spectrum of all nonzero algebra homomorphisms from , the algebra of all bounded type entire functions on , into . We endow with a structure of Riemann domain over whenever is symmetrically regular. The size of the fibers is also studied. Following the philosophy of (Aron et al., 1991), this is a step to study the set of all nonzero algebra homomorphisms from into of bounded holomorphic functions on the open unit ball of and of all nonzero algebra homomorphisms from into .
Reflection coefficient of inhomogeneous anisotropic impedance plane
Solved the problem of constructive synthesis of an inhomogeneous anisotropic impedance plane reflecting a homogeneous plane wave in two different preset directions on a matched and cross polarization. Obtained the reflection coefficients and expressions for the scattering diagrams. The impedance is implemented by the frequent array of orthogonal strips. The law of distribution of the reactance was obtained in an explicit form. It is shown that for arbitrarily given (unequal) directions of reflections on matched and cross polarizations, the orientation of the reactance strips turns out to be variable along the plane. Formulated restrictions on class of implemented scattering diagrams. Shown the results of numerical studies.