The Lebesgue constant for the space of functions of bounded p-variation

The principal part of the Lebesgue constant is determined, with a uniformly bounded remainder term, for the space of functions of bounded p-variation. 4 titles are cited.Translated from Matematicheskie Zametki, Vol. 2, No. 5, pp. 505–512, November, 1967.     

Nonlinear integral equations with respect to functions having bounded p-variation*

We prove an inequality for the p-variation, $ 1\leqslant p<1 $ , of Picard iterates associated to a nonlinear refinement Riemann–Stieltjes integral equation with respect to a possibly discontinuous function of bounded p-variation.     

Absolute convergence of double series of Fourier-Haar coefficients for functions of bounded p-variation

We consider functions of two variables of bounded p-variation of the Hardy type on the unit square. For these functions we obtain a sufficient condition for the absolute convergence of series of positive powers of Fourier coefficients with power-type weights with respect to the double Haar system. This condition implies those for the absolute convergence of series of Fourier-Haar coefficients of one-variable functions which have a bounded Wiener p-variation or belong to the class Lip ??. We show that the obtained results are unimprovable. We also formulate N-dimensional analogs of the main result and its corollaries.     

Superposition operators between weighted spaces of analytic functions

Abstract

We study the existence and the continuity of superposition operators between weighted spaces of holomorphic functions in terms of the weights.     

The p-variation of functions

A formula is derived for the p-variation of functions of the class Vq (1 q < p < ) and it is proved that this formula ceases to hold when 1 相似文献   

Power bounded operators and supercyclic vectors II

We show that each power bounded operator with spectral radius equal to one on a reflexive Banach space has a nonzero vector which is not supercyclic. Equivalently, the operator has a nontrivial closed invariant homogeneous subset. Moreover, the operator has a nontrivial closed invariant cone if belongs to its spectrum. This generalizes the corresponding results for Hilbert space operators.

For non-reflexive Banach spaces these results remain true; however, the non-supercyclic vector (invariant cone, respectively) relates to the adjoint of the operator.

     

Approximation of functions of bounded p-variation by means of polynomials of the Haar and Walsh systems

Translated from Matematicheskie Zametki, Vol. 53, No. 6, pp. 11–21, June, 1993.     

Hankel-type operators on the space of bounded harmonic functions

We study Hankel-type operators on the space of bounded harmonic functions on the open unit disk. These operators are related to tight uniform algebras, the Dunford-Pettis property, and Bourgain algebras.

     

Uniformly bounded Nemytskij operators between the Banach spaces of functions of bounded n-th variation

The main result says that the generator of any uniformly bounded composition operator acting between Banach algebras of functions of bounded n-th variation is an affine function with respect to the function variable.     

Laplace transforms of polynomially bounded vector-valued functions and semigroups of operators

We define an invariant of measure-theoretic isomorphism for dynamical systems, as the growth rate inn of the number of small -balls aroundα-n-names necessary to cover most of the system, for any generating partitionα. We show that this rate is essentially bounded if and only if the system is a translation of a compact group, and compute it for several classes of systems of entropy zero, thus getting examples of growth rates inO(n),O(n ^k ) fork ε ℕ, oro(f(n)) for any given unboundedf, and of various relationships with the usual notion of language complexity of the underlying topological system.     

Weakly compact composition operators between algebras of bounded analytic functions

We prove a characterization (up to the approximation property) of weakly compact composition operators in terms of their inducing analytic maps .

     

The PDE-preserving operators on nuclearly entire functions of bounded type

The PDE-preserving operators O on the space of nuclearly entire functions of bounded type H_Nb(E) on a Banach space E are characterized. An operator is PDE-preserving when it preserves homogenous solutions to homogeneous convolution equations. We establish a one to one correspondence between O and a set Σ of sequences of entire functionals, i.e. exponential type functions. In this way, algebraic structures on Σ, such as ring structures, can be carried over to O and vice versa. In particular, it follows that O is a non-commutative ring (algebra) with unity with respect to composition and the convolution operators form a commutative subring (subalgebra). We discuss range and kernel properties, for the operators in O, and characterize the projectors (onto polynomial spaces) in O by determining the corresponding elements in Σ. This revised version was published online in June 2006 with corrections to the Cover Date.     

SDEs with constraints driven by semimartingales and processes with bounded p-variation

We study the existence, uniqueness and stability of solutions of general stochastic differential equations with constraints driven by semimartingales and processes with bounded $p$-variation. Applications to SDEs with constraints driven by fractional Brownian motion and standard Brownian motion are given.     

Superposition operators between weighted Banach spaces of analytic functions of controlled growth

We characterize the entire functions which transform a weighted Banach space of holomorphic functions on the disc of type $H^{\infty }$ into another such space by superposition. We also show that all the superposition operators induced by such entire functions map bounded sets into bounded sets and are continuous. Superposition operators that map bounded sets into relatively compact sets are also considered.