Search results for "Bounded function"
showing 10 items of 508 documents
Banach spaces of general Dirichlet series
2018
Abstract We study when the spaces of general Dirichlet series bounded on a half plane are Banach spaces, and show that some of those classes are isometrically isomorphic between themselves. In a precise way, let { λ n } be a strictly increasing sequence of positive real numbers such that lim n → ∞ λ n = ∞ . We denote by H ∞ ( λ n ) the complex normed space of all Dirichlet series D ( s ) = ∑ n b n λ n − s , which are convergent and bounded on the half plane [ Re s > 0 ] , endowed with the norm ‖ D ‖ ∞ = sup Re s > 0 | D ( s ) | . If (⁎) there exists q > 0 such that inf n ( λ n + 1 q − λ n q ) > 0 , then H ∞ ( λ n ) is a Banach space. Further, if there exists a strictly increasing sequ…
Interpolating sequences for bounded analytic functions
2007
. We prove that any sequence in the open ball of a complex Banach space E, even in that of E**, whose norms are an interpolating sequence for H∞, is interpolating for the space of all bounded analytic functions on BE-The construction made yields that the interpolating functions depend linearly on the interpolated values.
A bilinear version of Orlicz–Pettis theorem
2008
Abstract Given three Banach spaces X, Y and Z and a bounded bilinear map B : X × Y → Z , a sequence x = ( x n ) n ⊆ X is called B -absolutely summable if ∑ n = 1 ∞ ‖ B ( x n , y ) ‖ Z is finite for any y ∈ Y . Connections of this space with l weak 1 ( X ) are presented. A sequence x = ( x n ) n ⊆ X is called B -unconditionally summable if ∑ n = 1 ∞ | 〈 B ( x n , y ) , z ∗ 〉 | is finite for any y ∈ Y and z ∗ ∈ Z ∗ and for any M ⊆ N there exists x M ∈ X for which ∑ n ∈ M 〈 B ( x n , y ) , z ∗ 〉 = 〈 B ( x M , y ) , z ∗ 〉 for all y ∈ Y and z ∗ ∈ Z ∗ . A bilinear version of Orlicz–Pettis theorem is given in this setting and some applications are presented.
Algebras with intermediate growth of the codimensions
2006
AbstractLet F be a field of characteristic zero and let A be an F-algebra. The polynomial identities satisfied by A can be measured through the asymptotic behavior of the sequence of codimensions and the sequence of colengths of A. For finite dimensional algebras we show that the colength sequence of A is polynomially bounded and the codimension sequence cannot have intermediate growth. We then prove that for general nonassociative algebras intermediate growth of the codimensions is allowed. In fact, for any real number 0<β<1, we construct an algebra A whose sequence of codimensions grows like nnβ.
Varieties of Algebras with Superinvolution of Almost Polynomial Growth
2015
Let A be an associative algebra with superinvolution ∗ over a field of characteristic zero and let $c_{n}^{\ast }(A)$ be its sequence of corresponding ∗-codimensions. In case A is finite dimensional, we prove that such sequence is polynomially bounded if and only if the variety generated by A does not contain three explicitly described algebras with superinvolution. As a consequence we find out that no intermediate growth of the ∗-codimensions between polynomial and exponential is allowed.
A generalized porous medium equation related to some singular quasilinear problems
2014
Abstract In this paper we study the existence and nonexistence of solutions for a Dirichlet boundary value problem whose model is { − ∑ m = 1 ∞ a m Δ u m = f in Ω u = 0 on ∂ Ω , where Ω is a bounded domain of R N , a m is a sequence of nonnegative real numbers, and f is in L q ( Ω ) , q > N 2 .
Derived length and character degrees of solvable groups
2003
We prove that the derived length of a solvable group is bounded in terms of certain invariants associated to the set of character degrees and improve some of the known bounds. We also bound the derived length of a Sylow p-subgroup of a solvable group by the number of different p-parts of the character degrees of the whole group.
A Hierarchy of Twofold Resource Allocation Automata Supporting Optimal Sampling
2009
We consider the problem of allocating limited sampling resources in a "real-time" manner with the purpose of estimating multiple binomial proportions. More specifically, the user is presented with `n ' sets of data points, S 1 , S 2 , ..., S n , where the set S i has N i points drawn from two classes {*** 1 , *** 2 }. A random sample in set S i belongs to *** 1 with probability u i and to *** 2 with probability 1 *** u i , with {u i }. i = 1, 2, ...n , being the quantities to be learnt. The problem is both interesting and non-trivial because while both n and each N i are large, the number of samples that can be drawn is bounded by a constant, c . We solve the problem by first modelling it a…
Two-Sided Estimates of the Solution Set for the Reaction–Diffusion Problem with Uncertain Data
2009
We consider linear reaction–diffusion problems with mixed Dirichlet–Neumann–Robin conditions. The diffusion matrix, reaction coefficient, and the coefficient in the Robin boundary condition are defined with an uncertainty which allow bounded variations around some given mean values. A solution to such a problem cannot be exactly determined (it is a function in the set of “possible solutions” formed by generalized solutions related to possible data). The problem is to find parameters of this set. In this paper, we show that computable lower and upper bounds of the diameter (or radius) of the set can be expressed throughout problem data and parameters that regulate the indeterminacy range. Ou…
PARAMETER BOUNDED ESTIMATION FOR QUASISPECIES MODELS OF MOLECULAR EVOLUTION
2006
Abstract The Quasispecies models identification for Evolutionary Dynamics is considered in a worst-case deterministic setting. These models analyze the DNA and RNA evolution or describe the population dynamics of viruses and bacteria. In this paper we identify the Fitness and the Replication Probability parameters of a genetic sequences, subject to a set of stringent constraints to have physical meaning and to guarantee positiveness. The conditional central estimate and the Uncertainty Intervals are determined. The effectiveness of the proposed procedure has been illustrated by means of simulation experiments while tests on real data are under concern.