Orthogonal systems invariant under an automorphism

, , - ( ) . , - , ( ) .     

Schatten class composition operators on weighted Bergman spaces of bounded symmetric domains

Summary We obtain trace ideal criteria for 0A ² () of a Bounded symmetric diomain in _n.     

The Laplacian with Robin Boundary Conditions on Arbitrary Domains

Using a capacity approach, we prove in this article that it is always possible to define a realization of the Laplacian on L ²() with generalized Robin boundary conditions where is an arbitrary open subset of R ⁿ and is a Borel measure on the boundary of . This operator generates a sub-Markovian C ₀-semigroup on L ²(). If d=d where is a strictly positive bounded Borel measurable function defined on the boundary and the (n–1)-dimensional Hausdorff measure on , we show that the semigroup generated by the Laplacian with Robin boundary conditions has always Gaussian estimates with modified exponents. We also obtain that the spectrum of the Laplacian with Robin boundary conditions in L ^p () is independent of p[1,). Our approach constitutes an alternative way to Daners who considers the (n–1)-dimensional Hausdorff measure on the boundary. In particular, it allows us to construct a conterexample disproving Daners' closability conjecture.     

Integrability of double trigonometric series with special coefficients

- , , . , L ¹=L ¹([0, ]×]0, ]). , ; , L ¹ , - . . . . 1976 ., ; 1989 .

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The basic part of this research was done while the author was a visiting professor at the Syracuse University, U.S.A., during the academic year 1986/87.     

On strong summability of polynomial expansions

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Dedicated to Professor L. Leindler on his 50^th birthday     

Notes on best constants in some Sobolev inequalities

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Nonparametric Inference for a Class of Stochastic Partial Differential Equations II

Consider the stochastic partial differential equationdu (t,x) = (t)u (t, x)dt + dW _Q(t,x), 0 t T where = ₂/x ₂, and is a class of positive valued functions. We obtain an estimator for the linear multiplier (t) and establish the consistency, rate of convergence and asymptotic normality of this estimator as 0.     

Two classes of conformally flat contact metric 3-manifolds

We give a classification of 3—dimensional conformally flat contact metric manifolds satisfying: =0(=L g) orR(Y, Z)=k[(Z)Y–(Y)Z]+[(Z)hY]–(Y)hZ] wherek and are functions. It is proved that they are flat (the non-Sasakian case) or of constant curvature 1 (the Sasakian case).     

μ-Reducible Languages

A word w is said to be a primitive word if it cannot be expressed as a power of any other word. A language L consisting of non-empty words is called -reducible if there exists a non-empty word w such that Lw contains only finitely many powers of each primitive word. We show that every regular component, context-free component, local language and every regular language containing no primitive words are -reducible. Languages which are not -reducible are investigated and characterized. We show that every code is -reducible. But there are 2-codes which are not -reducible. The -annihilator of a language L is the set of all non-empty words w such that Lw contains only finitely many powers of each primitive word. This paper also concerns the properties of the -annihilators of languages. The -annihilators of 2-codes and some other languages are investigated and characterized in this paper. The results provide an outline of the relationship between the catenation of languages and the powers of primitive words.     

On convergence of multiparameter strong submartingales in Banach lattices

- , ., B - — , B- {M _n ,nN ^d } n. .     

A Nonlinear Problem Associated to the Motion of a Membrane

A nonlinear model associated to the motion of a membrane is considered as limit of a sequence of approximate models, for which a global existence and uniqueness theorem can be proved. The paper investigates the relationship between the solutions of the real and approximate models.     

The Choquet-Deny convolution equation μ=μ*σ for probability measures on Abelian semigroups

In this note, we characterize the regular probability measures satisfying the Choquet-Deny convolution equation =* on Abelian topological semigroups for a given probability measure .     

Асимптоический Анализ Распределения Статистики Диксона

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On Almost β-Continuous Functions

A subset A of a topological space is said to be -open [1] if A Cl(Int(Cl(A))). A function f : X Y is said to be almost -continuous [18] if for each point x X and each open neighbourhood V of f(x) there exists a -open set U containing x such that f(U) Int(Cl(V)). Some new characterizations and several fundamental properties are obtained.     

The Orders of Related Elements of a Finite Field

All finite fields q (q 2, 3, 4, 5, 7, 9, 13, 25, 121) contain a primitive element for which + 1/ is also primitive. All fields of square order q ² (q 3, 5) contain an element of order q + 1 for which + 1/ is a primitive element of the subfield q. These are unconditional versions of general asymptotic results.     

On the exactness of a theorem of G.A. Fomin

, . . [1] - . .     

Approximation of functions of several variables by trigonometric polynomials with given number of harmonics,and estimates of ε-entropy

. - . .. . . . , 340 048 . 1      

A Hubert space characterization among function spaces

— [0,1] ,E — - e=1 [0,1]. I — _E =1, E=L ₂ x _e =xL ₂ x E.

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This work was prepared when the second author was a visiting professor of the CNR at the University of Firenze. He was supported by the Soros International Fund.     

An addendum to the paper “ranges of values of systems of functionals in certain classes of regular functions”

One gives an application of the results of the paper mentioned in the title to the problem of the range of the system of initial coefficients on the class V_k,(k2, 0<1) of functions f(z)=z+a₂z²+..., regular in ¦z¦<1, f(z)f(z)/z0 in ¦z¦<1, satisfying the condition ₀ ² ReJ(eⁱ)dk, 0<<1, where J(z)=(1+zf(z)/f(z)) +(1–+)zf(z)/f(z).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 154, pp. 31–35, 1986.     

On extremal subspaces and approximation of periodic functions by splines of minimal defect

. . , 320 625 . 72