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Displaying 81 –
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118
We give a method for constructing functions and for which has a specified subharmonic minorant . By a theorem of B. Cole,
this procedure establishes integral mean inequalities for conjugate functions. We apply
this method to deduce sharp inequalities for conjugates of functions in the class
, for . In particular, the case yields an improvement of Pichorides’ form of Zygmund’s classical inequality for the
conjugates of functions in . We also apply the method to produce a new proof of
the...
We consider a compact set K ⊂ ℝ in the form of the union of a sequence of segments. By means of nearly Chebyshev polynomials for K, the modulus of continuity of the Green functions is estimated. Markov’s constants of the corresponding set are evaluated.
The most important results of standard Calderón-Zygmund theory have recently been extended to very general non-homogeneous contexts. In this survey paper we describe these extensions and their striking applications to removability problems for bounded analytic functions. We also discuss some of the techniques that allow us to dispense with the doubling condition in dealing with singular integrals. Special attention is paid to the Cauchy Integral.[Proceedings of the 6th International Conference on...
Ever since the discovery of the connection between the Menger-Melnikov curvature and the Cauchy kernel in the L2 norm, and its impressive utility in the analytic capacity problem, higher dimensional analogues have been coveted. The lesson from 1-sets was that any such (nontrivial, nonnegative) expression, using the Riesz kernels for m-sets in Rn, even in any Lk norm (k ∈ N), would probably carry nontrivial information on whether the boundedness of these kernels in the appropriate norm implies rectifiability...
We discuss problems on Hankel determinants and the classical moment problem related to and inspired by certain Vandermonde determinants for polynomial interpolation on (quadratic) algebraic curves in ℂ².
We give a new proof, relying on polynomial inequalities and some aspects of potential theory, of large deviation results for ensembles of random hermitian matrices.
We present a number of Wiener’s type necessary and sufficient conditions (in terms of divergence of integrals or series involving a condenser capacity) for a compact set E ⊂ ℂ to be regular with respect to the Dirichlet problem. The same capacity is used to give a simple proof of the following known theorem [2, 6]: If E is a compact subset of ℂ such that for 0 < t ≤ 1 and a ∈ E, where d(F) is the logarithmic capacity of F, then the Green function of ℂ E with pole at infinity is Hölder continuous....
We develop a new method to prove asymptotic zero distribution for different kinds of
orthogonal polynomials. The method directly uses the orthogonality relations. We
illustrate the procedure in four cases: classical orthogonality, non-Hermitian
orthogonality, orthogonality in rational approximation of Markov functions and its non-
Hermitian variant.
2000 Mathematics Subject Classification: 30B40, 30B10, 30C15, 31A15.We are concerned with overconvergent power series. The main idea is to relate the distribution of the zeros of subsequences of partial sums and the phenomenon of overconvergence. Sufficient conditions for a power series to be overconvergent in terms of the distribution of the zeros of a subsequence are provided, and results of Jentzsch-Szegö type about the asymptotic distribution of the zeros of overconvergent subsequences are stated....
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