Related papers: On Similarity
We consider generalizations of Dunkl's differential-difference operators associated with groups generated by reflections. The commutativity condition is equivalent to certain functional equations. These equations are solved in many cases.…
On the basis of the explicit formulae for the action of the unitary group of exponentials corresponding to almost solvable extensions of a given closed symmetric operator with equal deficiency indices, we derive a new representation for the…
A theoretical framework is presented for a (copula-based) notion of dissimilarity between continuous random vectors and its main properties are studied. The proposed dissimilarity assigns the smallest value to a pair of random vectors that…
Filinski constructed a symmetric lambda-calculus consisting of expressions and continuations which are symmetric, and functions which have duality. In his calculus, functions can be encoded to expressions and continuations using primitive…
In this paper we obtain a set of five new transmutations of the mother formula. Further, we obtain the second set of ten exact metafunctional equations by crossbreeding on every two elements of the previous set. Elements of the last set…
Many combinatorial generating functions can be expressed as combinations of symmetric functions, or extracted as sub-series and specializations from such combinations. Gessel has outlined a large class of symmetric functions for which the…
We study the so-called John-Nirenberg space that is a generalization of functions of bounded mean oscillation in the setting of metric measure spaces with a doubling measure. Our main results are local and global John-Nirenberg…
In this paper, we study the Jacobi frame approximation with equispaced samples and derive an error estimation. We observe numerically that the approximation accuracy gradually decreases as the extended domain parameter $\gamma$ increases in…
We discuss Donsker's delta function within the framework of White Noise Analysis, in particular its extension to complex arguments. With a view towards applications to quantum physics we also study sums and products of Donsker's delta…
For a long time it has been a challenging goal to identify all orthogonal polynomial systems that occur as eigenfunctions of a linear differential equation. One of the widest classes of such eigenfunctions known so far, is given by…
Data cohesion, a recently introduced measure inspired by social interactions, uses distance comparisons to assess relative proximity. In this work, we provide a collection of results which can guide the development of cohesion-based methods…
This paper provides some first steps in developing empirical process theory for functions taking values in a vector space. Our main results provide bounds on the entropy of classes of smooth functions taking values in a Hilbert space, by…
Starting with a known polynomial identity, we derive two generalizations of Touchard's identity concerning Catalan numbers; one obtained using the Beta function and the other via a connection with Stirling numbers of the second kind. We…
Cosmological correlators encode invaluable information about the wavefunction of the primordial universe. In this letter we present a duality between correlators and wavefunction coefficients that is valid to all orders in the loop…
This paper provides a new similarity detection algorithm. Given an input set of multi-dimensional data points, where each data point is assumed to be multi-dimensional, and an additional reference data point for similarity finding, the…
To a function with values in the power set of a pre--ordered, separated locally convex space a family of scalarizations is given which completely characterizes the original function. A concept of a Legendre--Fenchel conjugate for set-valued…
This papers presents a generalization of the Weitzman overlapping coefficient, originally defined for two probability density functions, to a setting involving k independent distributions, denoted by Delta. To estimate this generalized…
Social inequality manifested across different strata of human existence can be quantified in several ways. Here we compute non-entropic measures of inequality such as Lorenz curve, Gini index and the recently introduced $k$ index…
Classification is a core topic in functional data analysis. A large number of functional classifiers have been proposed in the literature, most of which are based on functional principal component analysis or functional regression. In…
Schr{\"o}dinger noticed in 1952 that a scalar complex wave function can be made real by a gauge transformation. The author showed recently that one real function is also enough to describe matter in the Dirac equation in an arbitrary…