1,720,973 research outputs found
Onto Interpolation for the Dirichlet Space and for
Full text linkWe give a characterization of onto interpolating sequences with finite
associated measure for the Dirichlet space in terms of condenser capacity. In
the Sobolev space we define a natural notion of onto
interpolation and we prove that the same condenser capacity condition
characterizes all onto interpolating sequences. As a result, for sequences with
finite associated measure, the problem of interpolation by an analytic function
reduces to a problem of interpolation by a function in .Comment: 34 page
Riesz capacities of a set due to Dobi\'nski
Full text linkWe study the Riesz -capacity of the so called Dobi\'nski set. We
characterize the values of the parameters and for which the
-Riesz capacity of the Dobi\'nski set is positive. In particular we show
that the Dobi\'nski set has positive logarithmic capacity, thus answering a
question of Dayan, Fernand\'ez and Gonz\'alez. We approach the problem by
considering the dyadic analogues of the Riesz -capacities which seem to
be better adapted to the problem.Comment: 7 page
On the boundedness of generalized integration operators on Hardy spaces
Full text linkWe study the boundedness and compactness properties of the generalized
integration operator when it acts between distinct Hardy spaces in
the unit disc of the complex plane. This operator has been introduced by the
first author in connection to a theorem of Cohn about factorization of higher
order derivatives of functions in Hardy spaces. We answer in the affirmative a
conjecture stated in the same work, therefore giving a complete
characterization of the class of symbols for which the operator is bounded
from the Hardy space to Comment: 19 page
Totally null sets and capacity in Dirichlet type spaces
Full text linkIn the context of Dirichlet type spaces on the unit ball of ,
also known as Hardy-Sobolev or Besov-Sobolev spaces, we compare two notions of
smallness for compact subsets of the unit sphere. We show that the functional
analytic notion of being totally null agrees with the potential theoretic
notion of having capacity zero. In particular, this applies to the classical
Dirichlet space on the unit disc and logarithmic capacity. In combination with
a peak interpolation result of Davidson and the second named author, we obtain
strengthenings of boundary interpolation theorems of Peller and Khrushch\"{e}v
and of Cohn and Verbitsky.Comment: 20 page
Complete Pick Spaces: Theory and Examples
Full text linkThis thesis explores the Nevanlinna Pick problem in complex analysis, which involves finding an analytic function that interpolates given data points within the complex unit disc.
It focuses on reproducing kernel Hilbert spaces (RKHS) known as Pick spaces, which possess the analog of the interpolation property.
The main results of the thesis relate to the study of a concrete and simple RKHS of functions on the real line.
This space is completely characterized, with proofs of the Pick property, study of interpolating sequences, multipliers, Carleson measures, invariant subspaces, and the solution to the Corona problem
A note on simply interpolating sequences for the Dirichlet space
Full text linkWe study simply interpolating sequences for the Dirichlet space in the unit
disc. In particular we are interested in comparing three different sufficient
conditions for simply interpolating sequences. The first one is the the so
called one box condition, the second is the column bounded propererty for the
associated Grammian matrix and the third one is a restricted version of the one
box condition introduced by Bishop and, independently, by Marshall and
Sundberg. We prove that the one box condition implies the column bounded
property which in turn implies the restricted on box condition of
Bishop-Marshall-Sundberg, and we give two counterexamples which show that the
reverse implications fail even for weakly separated sequences.Comment: A critical error in the proof of the converse implication in the main
theorem in the first version of the paper (v1) has been spotted. We are now
able to provide a counterexample for this implicatio
Generalized integration operators on Hardy spaces
Full text linkInspired by the study of generalized Cesaro operator T_g introduced by Aleman and Siskakis we study a variation of this operator,namely P(g,a) , depending on an analytic symbol g and an n - tuple of complex numbers, a . Regarding the boundedness properties of this operator we prove that P(g,a) is a bounded linear operator from H^p to itself if and only if g is an analytic function of bounded mean oscillation and compact if and only if g is of vanishing mean oscillation. Furthermore in the special case n=2, a=0 we completely characterized the functions g for which P(g,a) is bounded from H^p to H^q, 0<p,q. As an application of our theorem we prove a factorization theorem for any derivative of an function, and also a theorem about solutions of complex linear differential equations.Inom komplex analys och operatorteori studerar man vanligtvis begränsade linjära operatorer mellan Banachrum bestående av analytiska funktioner. Detta görs för att kunna erhålla information om själva Banachrummets struktur. Ett klassiskt exempel är Cesaros medelvärdes operator på H^p , ett Hardyrum bestående av analytiska funktioner. En generalisering av denna operator är det så kallade Cesaros generaliserad operator, Tg , som kan spåras tillbaka till arbetet av Ch. Pommerenke, 1970. Operatorns egenskaper har varit ett aktivt forskningsområde i de senaste 20 åren. I detta arbete, som är inspirerad av studien av Tg , försöker vi ge svar till några frågor angående operatorns variation
Carleson measures for Hardy-Sobolev spaces in the Siegel upper half-space
Full text linkWe give a capacitary type characterization of Carleson measures for a class
of Hardy-Sobolev spaces (also known as weighted Dirichlet spaces) on the Siegel
upper half-space, introduced by Arcozzi et al. This answers in part a question
raised by the same authors
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
- …
