On sequences of Dirichlet polynomials uniformly bounded on half planes

Given and a sequence of Dirichlet polynomials estimates for the coefficientsa _n are proved if {_n} is uniformly bounded on a region containing a half plane. Thereby a result is obtained which is an analogue of a known result for polynomials, that is for theA-transforms of the geometric sequence; moreover a Jentzsch type theorem for {_n(z)} is derived.     

A classification of martingale Hardy spaces associated with rearrangement-invariant function spaces

Let X be a rearrangement-invariant Banach function space over a complete probability space , and denote by the Hardy space consisting of all martingales such that . We prove that implies for any filtration if and only if Doobs inequality holds in X, where denotes the martingale defined by , n = 0, 1, 2, ..., and a.s.Received: 1 August 2000     

On transformations z(t) = y(ϕ(t)) of ordinary differential equations

The paper describes the general form of an ordinary differential equation of the order n + 1 (n 1) which allows a nontrivial global transformation consisting of the change of the independent variable. A result given by J. Aczél is generalized. A functional equation of the form where are given functions, is solved on .     

On dualities between function spaces

By [6], the dualities between and , whereX andW are two sets and (i.e., the mappings satisfying for all and all index setsI), can be represented with the aid of functions . Here we show that they can be also represented with the aid of functions , whereR = (–, +). As an application, we show that every duality is completely determined by a suitable duality between 2 ^{X ×R} and 2 ^{W ×R} (i.e., a mapping 2 ^{X ×R} 2 ^{W ×R} satisfying for all {M _i} _iI 2 ^{X ×R} and all index setsI), applied to the epigraphs of the functions .     

A stability test for real polynomials

Summary By the argument principle the number of zeros inside of the unit circle of a real polynomial , can be estimated by the variation of the argument ofp _n (exp(it)) ift varies from 0 to . This variation has its maximal value n iff then distinct zeros of are separated by then–1 distinct zeros of . Now from Sturm sequence techniques in connection with special properties of the Chebyshev polynomials there results a very simple stability test.Dedicated to Professor Dr. Wilhelm Niethammer on his sixtieth birthday (December 2, 1993)     

Hyponormality of Toeplitz Operators with Polynomial and Symmetric-Type Symbols

Suppose that is a trigonometric polynomial of the form (z) = ^N_n=-N a_n zⁿ. It is well-known that T is normal if and only if | a_{– N}| =  | a_N| and the Fourier coefficients of satisfy the following symmetry condition:

On the Boundedness of a Recurrence Sequence in a Banach Space

We investigate the problem of the boundedness of the following recurrence sequence in a Banach space B: where |y _n} and | _n } are sequences bounded in B, and A _k, k 1, are linear bounded operators. We prove that if, for any > 0, the condition is satisfied, then the sequence |x _n} is bounded for arbitrary bounded sequences |y _n} and | _n } if and only if the operator has the continuous inverse for every z C, |z| 1.     

Reducibility of lacunary polynomials,VII

Letk>1 and let be non-zero algebraic numbers contained in the field . It is shown that for almost all, in the sense of density integer vectorsn ₁,...,n _k the polynomial becomes irreducible over on dividing by the product of all factorsx–, where is a root of unity.Dedicated to Professor E. Hlawka on the occasion of his seventieth birthday     

Characterization of Normal Traces on Von Neumann Algebras by Inequalities for the Modulus

It is proved that if a normal semifinite weight on a von Neumann algebra satisfies the inequality for any selfadjoint operators in , then this weight is a trace. Several similar characterizations of traces among the normal semifinite weights are proved. In particular, Gardner's result on the characterization of traces by the inequality is refined and reinforced.     

A new bound for an extension of Mason’s theorem for functions of several variables

In this paper, using the generalized Wronskian, we obtain a new sharp bound for the generalized Masons theorem [1] for functions of several variables. We also show that the Diophantine equation (The generalized Fermat-Catalan equation) where , such that k out of the n-polynomials are constant, and under certain conditions for has no non-constant solution. Received: 20 March 2003     

The Expected Number of Local Maxima of a Random Algebraic Polynomial

In this work we obtain an asymptotic estimate for the expected number of maxima of the random algebraic polynomial , where a _j (j=0, 1,...,n–1) are independent, normally distributed random variables with mean and variance one. It is shown that for nonzero , the expected number of maxima is asymptotic to log n, when n is large.     

The Spectrum of the C*-Algebra of Pseudodifferential Boundary Value Problems on a Manifold with Smooth Edges

The C ^*-algebra generated by the operators of pseudodifferential boundary value problems on a manifold with smooth closed disjoint edges and boundary is studied. The operators act in the space L ₂( ) L ₂( ). The goal of this paper is to describe all (up to an equivalence) irreducible representations of the algebra Bibliography: 12 titles.     

Nonuniqueness Sequences for Weighted Algebras of Holomorphic Functions in the Unit Circle

Suppose that is a system of continuous subharmonic functions in the unit disk and is the class of holomorphic functions f in such that log|f(z)| ≤ B _f p _f (z) + C _f , z ∈ , where B _f and C _f are constants and p _f ∈ . We obtain sufficient conditions for a given number sequence Λ = { λ_n} ⊂ to be a subsequence of zeros of some nonzero holomorphic function from , i.e., Λ is a nonuniqueness sequence for .__________Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 775–787.Original Russian Text Copyright ©2005 by L. Yu. Cherednikova.     

The First-Order Nonholonomic Connections with the Galilean Groups of Local Transformations. II

In the canonical smooth fiber bundles endowed with the metric tensor fields of relevant structure, we consider natural representations of the Galilean groups and construct -invariant generalizations of differentiable connections. In both regular and special cases of the representations of the relevant groups , we found all the affine nonholonomic -, -, and -connections of the first order (see [1]–[3]) possessing the local Lie groups of transformations and also described the respective -invariant planar connections.     

True Dimension of Some Binary Quadratic Trace Goppa Codes

We compute in this paper the true dimension over of Goppa Codes (L, g) defined by the polynomial proving, this way, a conjecture stated in [14,16].     

On Fraenkel’s <Emphasis Type="Italic">N</Emphasis>-Heap Wythoff’s Conjectures

The N-heap Wythoffs game is a two-player impartial game with N piles of tokens of sizes Players take turns removing any number of tokens from a single pile, or removing (a₁,..., a_N) from all piles - a_i tokens from the i-th pile, providing that where is the nim addition. The first player that cannot make a move loses. Denote all the P-positions (i.e., losing positions) by Two conjectures were proposed on the game by Fraenkel [7]. When are fixed, i) there exists an integer N₁ such that when . ii) there exist integers N₂ and _2 such that when , the golden section.In this paper, we provide a sufficient condition for the conjectures to hold, and subsequently prove them for the three-heap Wythoffs game with the first piles having up to 10 tokens.AMS Subject Classification: 91A46, 68R05.     

Lattices of interpretability types of varieties

Let be the set of all primes, the field of all algebraic numbers, and Z the set of square-free natural numbers. We consider partially ordered sets of interpretability types such as , and , where AD is a variety of -divisible Abelian groups with unique taking of the pth root _p(x) for every p , is a variety of -modules over a normal field , contained in , and G_n is a variety of n-groupoids defined by a cyclic permutation (12 ...n). We prove that , and are distributive lattices, with and where ub and ub_f are lattices (w.r.t. inclusion) of all subsets of the set and of finite subsets of , respectively.Deceased.__________Translated from Algebra i Logika, Vol. 44, No. 2, pp. 198–210, March–April, 2005.     

On the Number of Subgraphs of a Specified Form Embedded in a Random Graph

Let U ₁, U ₂,... be a sequence of i.i.d. random elements in R^d. For x>0, a graph G _n (x) may be formed by connecting with an edge each pair of points in that are separated by a distance no greater than x. The points of G _n (x) could represent the stations in a telecommunications network and the edge set the lines of communication that exist among them. Let be a collection of graphs on mn points having a specified form or structure, and let denote the number of subgraphs embedded in G _n (x) and contained in . It is shown that a SLLN, CLT and LIL for follow easily from the theory of U-statistics. In addition, a uniform (in x) SLLN is proved for collections that satisfy a certain monotonicity condition. Some applications are mentioned and the results of some simulations presented. The scaling constants appearing in the CLT are usually hard to obtain. These are worked out for some special cases.     

Entire Dirichlet Series of Rapid Growth and New Estimates for the Measure of Exceptional Sets in Theorems of the Wiman–Valiron Type

For entire Dirichlet series of the form , we establish conditions under which the relation

A Product Formula Related to Quantum Zeno Dynamics

We prove a product formula which involves the unitary group generated by a semibounded self-adjoint operator and an orthogonal projection P on a separable Hilbert space with the convergence in It gives a partial answer to the question about existence of the limit which describes quantum Zeno dynamics in the subspace Ran P. The convergence in is demonstrated in the case of a finite-dimensional P. The main result is illustrated in the example where the projection corresponds to a domain in and the unitary group is the free Schrödinger evolution.submitted 21/06/04, accepted 12/10/04