ترغب بنشر مسار تعليمي؟ اضغط هنا

Constructing measures with identical moments

98   0   0.0 ( 0 )
 نشر من قبل Alexey Kuznetsov
 تاريخ النشر 2016
  مجال البحث
والبحث باللغة English
 تأليف Alexey Kuznetsov




اسأل ChatGPT حول البحث

The Nevanlinna parametrization establishes a bijection between the class of all measures having a prescribed set of moments and the class of Pick functions. The fact that all measures constructed through the Nevanlinna parametrization have identical moments follows from the theory of orthogonal polynomials and continued fractions. In this paper we explore the opposite direction: we construct a set of measures and we show that they all have identical moments, and then we establish a Nevanlinna-type parametrization for this set of measures. Our construction does not require the theory of orthogonal polynomials and it exposes the analytic structure behind the Nevanlinna parametrization.

قيم البحث

اقرأ أيضاً

We study the general moment problem for measures on the real line, with polynomials replaced by more general spaces of entire functions. As a particular case, we describe measures that are uniquely determined by a restriction of their Fourier transfo rm to a finite interval. We apply our results to prove an extension of a theorem by Eremenko and Novikov on the frequency of oscillations of measures with a spectral gap (high-pass signals) near infinity.
145 - Benoit F. Sehba 2016
We give in this paper some equivalent definitions of the so called $rho$-Carleson measures when $rho(t)=(log(4/t))^p(loglog(e^4/t))^q$, $0le p,q<infty$. As applications, we characterize the pointwise multipliers on $LMOA(mathbb S^n)$ and from this sp ace to $BMOA(mathbb S^n)$. Boundedness of the Ces`aro type integral operators on $LMOA(mathbb S^n)$ and from $LMOA(mathbb S^n)$ to $BMOA(mathbb S^n)$ is considered as well.
In this note, we obtain a full characterization of radial Carleson measures for the Hilbert-Hardy space on tube domains over symmetric cones. For large derivatives, we also obtain a full characterization of the measures for which the corresponding em bedding operator is continuous. Restricting to the case of light cones of dimension three, we prove that by freezing one or two variables, the problem of embedding derivatives of the Hilbert-Hardy space into Lebesgue spaces reduces to the characterization of Carleson measures for Hilbert-Bergman spaces of the upper-half plane or the product of two upper-half planes.
For rational functions, we use simple but elegant techniques to strengthen generalizations of certain results which extend some widely known polynomial inequalities of Erdos-Lax and Turan to rational functions R. In return these reinforced results, i n the limiting case, lead to the corresponding refinements of the said polynomial inequalities. As an illustration and as an application of our results, we obtain some new improvements of the Erdos-Lax and Turan type inequalities for polynomials. These improved results take into account the size of the constant term and the leading coefficient of the given polynomial. As a further factor of consideration, during the course of this paper we shall demonstrate how some recently obtained results due to S. L. Wali and W. M. Shah, [Some applications of Dubinins lemma to rational functions with prescribed poles, J. Math.Anal.Appl.450 (2017) 769-779], could have been proved without invoking the results
Minimum Riesz energy problems in the presence of an external field are analyzed for a condenser with touching plates. We obtain sufficient and/or necessary conditions for the solvability of these problems in both the unconstrained and the constrained settings, investigate the properties of minimizers, and prove their uniqueness. Furthermore, characterization theorems in terms of variational inequalities for the weighted potentials are established. The results obtained are illustrated by several examples.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا