1,720,995 research outputs found
Weyl asymptotics for tensor products of operators and Dirichlet divisors
Full text linkWe study the counting function of the eigenvalues for tensor products of operators, and their perturbations, in the context of Shubin classes and closed manifolds. We emphasize connections with problems of analytic number theory, concerning in particular generalized Dirichlet divisor functions
On Temperate Distributions Decaying at Infinity
No full textWe describe classes of temperate distributions with prescribed decay properties at infinity. The definition of the elements of such classes is given in terms of the Schwartz’ bounded distributions, and we discuss their characterization in terms of convolution and of decomposition as a finite sum of derivatives of suitable functions. We also prove mapping properties under the action of a class of Fourier integral operators, with inhomogeneous phase function and polynomially bounded symbol globally defined on R
The structure of quasiasymptotics of Schwartz distributions
Full text linkIn this article complete characterizations of quasiasymptotic behaviors of Schwartz distributions are presented by means of structural theorems. The cases at infinity and the origin are both analyzed. Special attention is paid to the quasiasymptotic of degree -1 and it is shown how the structural theorem can be used to study Ces\`{a}ro and Abel summability of trigonometric series and integrals. Further properties of quasiasymptotics at infinity are discussed, the author presents a condition over test functions which allows one to evaluate them at the quasiasymptotic, these test functions are in bigger spaces than . An extension of the structural theorems for quasiasymptotics is given, the author studies a structural characterization of the behavior in , where is a regularly varying function
An elementary approach to asymptotic behavior in the Ces\`{a}ro sense and applications to the Laplace and Stieltjes transforms
No full textGoing 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
On the non-triviality of certain spaces of analytic functions. Hyperfunctions and ultrahyperfunctions of fast growth
No full textOn Borel summability and analytic functionals
Full text linkAbstract. We show that a formal power series has positive radius of convergence if and only if it is uniformly Borel summable over a circle with center at the origin. Consequently, we obtain that an entire function f is of exponential type if and only if the formal power series ∞ n=0 f (n) (0)z n is uniformly Borel summable over a circle centered a the origin. We apply these results to obtain a characterization of those Silva tempered ultradistributions which are analytic functionals. We also use Borel summability to represent analytic functionals as Borel sums of their moment Taylor series over the Borel polygon
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