1,720,990 research outputs found
On a Solution of the Multidimensional Truncated Matrix-Valued Moment Problem
Full text link\ua9 2022, The Author(s). We will consider the multidimensional truncated p
7 p Hermitian matrix-valued moment problem. We will prove a characterisation of truncated p
7 p Hermitian matrix-valued multisequence with a minimal positive semidefinite matrix-valued representing measure via the existence of a flat extension, i.e., a rank preserving extension of a multivariate Hankel matrix (built from the given truncated matrix-valued multisequence). Moreover, the support of the representing measure can be computed via the intersecting zeros of the determinants of matrix-valued polynomials which describe the flat extension. We will also use a matricial generalisation of Tchakaloff’s theorem due to the first author together with the above result to prove a characterisation of truncated matrix-valued multisequences which have a representing measure. When p= 1 , our result recovers the celebrated flat extension theorem of Curto and Fialkow. The bivariate quadratic matrix-valued problem and the bivariate cubic matrix-valued problem are explored in detail
Multivariate moment indeterminateness: Separating functions and bounded point evaluations
No full text\ua9 2026 The Author(s). The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.The discrete data encoded in the power moments of a positive measure, fast decaying at infinity on Euclidean space, are incomplete for recovery, leading to the concept of moment indeterminateness. On the other hand, classical integral transforms (Fourier-Laplace, Fantappi\ue8, Poisson) of such measures are complete, often invertible via an effective inverse operation. The gap between the two non-uniqueness/uniqueness phenomena is manifest in the dual picture, when trying to extend the measure, regarded as a positive linear functional, from the polynomial algebra to the full space of continuous functions. This point of view was advocated by Marcel Riesz a century ago, in the single real variable setting. Notable advances in functional analysis have their root in Riesz\u27s celebrated four notes devoted to the moment problem. A key technical ingredient being there the monotone approximation by polynomials of kernels of integral transforms. With inherent new obstacles, we reappraise in the context of several real variables M. Riesz\u27s variational principle. The result is an array of necessary and sufficient moment indeterminateness criteria, some raising real algebra questions, as well as others involving intriguing analytic problems, all gravitating around the concept of moment separating function
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
The matricial subnormal completion problem
Full text link\ua9 2022 Elsevier Inc. Given a truncated sequence of positive numbers a=(aj)j=0m, the subnormal completion problem (originally posed and geometrically solved by J. Stampfli) asks whether or not there exists a subnormal weighted shift operator on ℓ2 whose initial weights are given by a. Subsequently a concrete solution based on a solution of the truncated Stieltjes moment problem was discovered by Curto and Fialkow. In this paper we will consider a matricial analogue of the subnormal completion problem, where the truncated sequence of positive numbers (aj)j=0m is replaced by a truncated sequence of positive definite matrices. We will provide concrete conditions for a solution based on the parity of m and make a connection with a matricial truncated Stieltjes moment problem. We will also put forward a certain canonical subnormal completion which is minimal in the sense of the norm of the corresponding weighted shift operator and describe the support of the corresponding matricial Berger measure in terms of the zeros of a matrix polynomial which describes the initial positive rank preserving extension
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
- …
