1,720,976 research outputs found
The Lusin area function and local admissible convergence of harmonic functions on homogeneous trees
Full text linkWe prove admissible convergence to the boundary of functions that are harmonic on a subset of a homogeneous tree by means of a discrete Green formula and an analogue of the Lusin area function
Approximate identities on some homogeneous Banach spaces
Full text linkWe study the geometric and approximation properties of Marcinkiewicz spaces
and Stepanoff spaces, , as well as others
where translations are not isometric but bounded (the bounded
-mean spaces) or even unbounded (\Mean0). We construct
a function that belongs to these spaces and has the unusual and unexpected property
that all approximate identities converge to
pointwise but they never converge in norm
Twist points of planar domains
No full textWe establish a potential theoretic approach to the study of twist points in the boundary of simply connected planar domains
A potential theoretic approach to twisting
No full textThis paper introduces a geometric, potential theoretic approach to the study of twist point in the boundary of a planar domain. It introduces a map h from a domain D to harmonic functions such that, when z tends to a boundary point w, the limit behaviour of h determines if w is a twist point or is sectorially accessible. The construction is based only on potential-theoretic methods and does not use the Riemann mapping theorem
Function Spaces with Bounded Lp Means and Their Continuous Functionals
Full text linkThis paper studies typical Banach and complete seminormed
spaces of locally summable functions and their continuous functionals. Such
spaces were introduced long ago as a natural environment to study almost periodic
functions (Besicovitch, 1932; Bohr and Fölner, 1944) and are defined by boundedness of suitable Lp means.
The supremum of such means defines a norm (or a seminorm, in the case of
the full Marcinkiewicz space) that makes the respective spaces complete.
Part of this paper is a review of the topological vector space structure,
inclusion relations, and convolution operators. Then we expand and improve the deep theory due to Lau of representation of continuous
functional and extreme points of the unit balls, adapt these results to
Stepanoff spaces, and present interesting examples of discontinuous functionals that
depend only on asymptotic values
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
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