In this note we prove the following theorem: Suppose and ω is an admissible weight distortion function ψ. Then there is a constant C=C(p,ω) such that abs(f(0))^p<
In this paper we define some new sublinear functions by considering a sequence of infinite matrices B = B_i. We prove some inequalities which extend the well ? known Knopp?s core theorem.
We give a version of Vidav Palmer?s theorem for m ? convex algebras. In the commutative case, we obtain a C* - l. m. c. a. structure.
In this paper, using the concept of H_u - semigroup, partial semihypergroup and partial abelian semigroup, we introduce the concept of partial abelian H_u ? monoid. This structure is more general than previously considered frameworks. Then we study relationships between congruences on partial abelian H_u ? monoids and prove some results in this connection.
The goal of this survey is to review some results concerning the deep relation between modular forms and ?geometric? Galois representations with values in GL(2,K) (K a p- adic field). Many questions in this classing setting remain open despite the momentous by Wiles and Taylor ? Wiles. One can even ask similar questions for more general automorphic forms like Siegel modular forms, replacing GL(2) by GSp(4); however this topic will not be touched in this paper, see [35]. This paper is a written version of a talk given in Anogia (Creta) during the third Panhellenic Conference in Number Theory and Algebra, Sept. 1-3, 2000.
Let A be a commutative algebra. We show that the sum of two spectral ideals is spectral. This result allows us to define new spectral ideals in a commutative algebra. We show also that an algebra with all its maximal commutative subalgebras spectral is not necessarily spectral. Finally, we will define the class of spectrally simple algebras.
In this paper we study the semicompleteness of the direct product GA of two groups A and B in relation to the semicompleteness of its direct factors. We give necessary and in some cases and sufficient conditions for the semicompleteness of the group.
In this work the modified Green?s ? function technique for the exterior two - dimensional Dirichlet problem is examined. We introduce a modification of the fundamental solution in order to remove the lack of uniqueness of solution of the boundary integral equation describing the problem. We establish the conditions that the coefficients of the modification must satisfy in order to overcome the non ? uniqueness problem. We also consider the special case of a circle choosing suitably the coefficients of optimization.
In this paper we prove a new fixed point theorem in Banach algebras via the measure of noncompactness and apply it for proving existence and continuous dependence results for certain nonlinear integral equations of mixed type in Banach algebras.
We show that for a Hilbert space X and Ω^n, the space of all compact convex subsets of R^n, endowed with the Hausdorff metric, each bounded uniformly continuous function from X to Ω^n can be approximated by Lipschitz functions.
By utilizing a combination of properties of the consequent mapping with the Brouwer?s fixed point theorem we obtain existence results for the nearly ? periodic boundary value problem.
Let (q(x),p(x)) be a doubly periodic Dirac potential; denote by L the lattice of its periods. The associated spectral curve is a (possibly singular) hyperelliptic covering of the elliptic curve C|L. We show that by varying L we can obtain a smooth spectral curve of the same genus.
A characterization of two parabolic subgroups of C_01 using the amalgamation method.
In this paper we use a method of O. Kolberg to prove the following congruence for moduli 5 and 7 for the convolution of divisor sum function