Hankel-Schur multipliers and multipliers of the space H1

In this paper there is given a sufficient condition for a Hankel matrix _F to belong to the space of Schur multipliers of all bounded operators in ² (or, what is the same, to the tensor algebra V²). It is shown that ifw is a nonnegative function on T, such that is a sequence of integers, {F_i}_j1 is a sequence of polynomials,) and, then _FV². It follows from this that under these conditions F is a multiplier of the space H¹, i.e.,.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 135, pp. 113–119, 1984     

H p multipliers on stratified groups

Summary In this paper we give a criterion for boundedness on the Hardy spaces for functions M() of the sublaplacian on a stratified group. The criterion requires that the function M satisfies locally a Besov condition. The proof is based on the atomic and molecular characterization of Hardy spaces.     

On universality of the Lerch zeta-function

It is known that the Lerch zeta-function L(λ, α, s) with transcendental parameter α is universal in the Voronin sense; i.e., every analytic function can be approximated by shifts L(λ, α, s + iτ) uniformly on compact subsets of some region. In this paper, the universality for some classes of composite functions F(L(λ, α, s)) is obtained. In particular, general theorems imply the universality of the functions sin(L(λ, α, s)) and sinh(L(λ, α, s)).     

On the spectrum of the C*-algebra of fourier multipliers in a cone

We describe the spectrum of the C^*-algebra generated by the Fourier multipliers (singular integral operators) on the space L₂ with a polynomial weight in an acute-angled convex cone of the space ⁿ. Bibliography: 12 titles.Translated fromProblemy Matematicheskogo Analiza, No. 12, 1992, pp. 61–82.     

On the universality of the nonstationary ideal

Burke proved that the generalized nonstationary ideal, denoted by NS, is universal in the following sense: every normal ideal, and every tower of normal ideals of inaccessible height, is a canonical Rudin‐Keisler projection of the restriction of NS to some stationary set. We investigate how far Burke's theorem can be pushed, by analyzing the universality properties of NS with respect to the wider class of ‐systems of filters introduced by Audrito and Steila. First we answer a question of Audrito and Steila, by proving that ‐systems of filters do not capture all kinds of set‐generic embeddings. We provide a characterization of supercompactness in terms of short extenders and canonical projections of NS, without any reference to the strength of the extenders; as a corollary, NS can consistently fail to canonically project to arbitrarily strong short extenders. We prove that ω‐cofinal towers of normal ultrafilters, e.g., the kind used to characterize I2 and I3 embeddings, are well‐founded if and only if they are canonical projections of NS. Finally, we provide a characterization of “ is Jónsson” in terms of canonical projections of NS.     

On the universality of the Riemann zeta-function

The research has been partially supported by Grant N LAC000 from the International Science Foundation.     

On multipliers on compact Lie groups

In this note we announce L ^p multiplier theorems for invariant and noninvariant operators on compact Lie groups in the spirit of the well-known Hörmander-Mikhlin theorem on ? ⁿ and its versions on the torus $\mathbb{T}^n$ . Applications to mapping properties of pseudo-differential operators on L ^p -spaces and to a priori estimates for nonhypoelliptic operators are given.     

Riesz multipliers onL 1 (G)

This work was supported in part by the Italian Research Science Foundation (C.N.R.), Fondi Ministeriali 40%, 1986.     

On the Taylor spectrum of left-right multipliers

The Taylor spectrum of a mixed pair of multiplication operators is determined on an ultraprime Banach algebra.

     

On the joint universality of periodic zeta functions

In this paper, we obtain the joint universality (in the sense of Voronin) of Dirichlet series with periodic multiplicative coefficients. The proof is based on a joint limit theorem in the space of analytic functions.     

On the joint universality of Lerch zeta functions

In the paper, a Voronin-type joint universality theorem for Lerch zeta functions is obtained under weaker assumptions than those in A. Laurin?ikas and K. Matsumoto, “Joint value distribution theorems on Lerch zeta-functions. III,” in Analytic and Probabilistic Methods in Number Theory (TEV, Vilnius, 2007), pp. 87–98.     

On the simpleness of zeros of Stokes multipliers

The aim of this paper is to discuss the simpleness of zeros of Stokes multipliers associated with the differential equation -Φ^″(X)+W(X)Φ(X)=0, where W(X)=X^m+a₁X^m-1+?+a_m is a real monic polynomial. We show that, under a suitable hypothesis on the coefficients a_k, all the zeros of the Stokes multipliers are simple.     

The question on multipliers in L 1 and C

The connection between Belinsky?CDveyrin?CMalamud??s theorem on multipliers and some other known theorems on multipliers in the spaces L ¹ and C is clarified. It is shown that Belinsky?CDveyrin?CMalamud??s theorem can be obtained from them. The relevant examples of multipliers in the spaces L ¹ and C indicating the nonequivalence of the compared theorems are presented.     

Spherical Harmonic Analysis for Spinors on H n (C)

Recent results on the harmonic analysis of spinor fields on the complex hyperbolic space H ⁿ (C) are reviewed. We discuss the action of the invariant differential operators on the Poisson transforms, the theory of spherical functions and the spherical transform. The inversion formula, the Paley–Wiener theorem, and the Plancherel theorem for the spherical transform are obtained by reduction to Jacobi analysis on L ²(R).     

On Lagrange multipliers of trust-region subproblems

Trust-region methods are globally convergent techniques widely used, for example, in connection with the Newton’s method for unconstrained optimization. One of the most commonly-used iterative approaches for solving trust-region subproblems is the Steihaug–Toint method which is based on conjugate gradient iterations and seeks a solution on Krylov subspaces. This paper contains new theoretical results concerning properties of Lagrange multipliers obtained on these subspaces. AMS subject classification (2000)  65F20