Related papers: Analytic Functional Calculus in Quaternionic Frame…
It is well known that a non-constant complex-valued function $f$ defined on the open unit disk $\mathbb D$ is an analytic self-mapping of $\D$ if and only if Pick matrices $\left[…
We present a Riesz-like hyperholomorphic functional calculus for a set of non-commuting operators based on the Clifford analysis. Applications to the quantum field theory are described. Keywords: Functional calculus, Weyl calculus, Riesz…
Operator $k$-tone functions on an open interval of the real line, which are higher order extensions of operator monotone and convex functions, are characterized via certain inequalities for the real and imaginary parts of analytic…
We introduce a total order and the absolute value function for dual numbers. The absolute value function of dual numbers are with dual number values, and have properties similar to the properties of the absolute value function of real…
This work looks at the theory of octonionic slice regular functions through the lens of differential topology. It proves a full-fledged version of the Open Mapping Theorem for octonionic slice regular functions. Moreover, it opens the path…
Linear algebra computations are foundational for neural networks and machine learning, often handled through arrays. While many functional programming languages feature lists and recursion, arrays in linear algebra demand constant-time…
A set of exactly computable orthonormal basis functions that are useful in computations involving constituent quarks is presented. These basis functions are distinguished by the property that they fall off algebraically in momentum space…
The theory of slice regular functions of a quaternionic variable, introduced in 2006 by Gentili and Struppa, extends the notion of holomorphic function to the quaternionic setting. This fast growing theory is already rich of many results…
In this paper we first recall the definition of an octonion algebra and its algebraic properties. We derive the so called $e_4$-calculus and using it we obtain the list of generalized Cauchy-Riemann systems in octonionic monogenic…
In this paper we study generalized J-inner matrix valued functions which appear as resolvent matrices in various indefinite interpolation problems. Reproducing kernel indefinite inner product spaces associated with a generalized J-inner…
We study functional graphs generated by quadratic polynomials over prime fields. We introduce efficient algorithms for methodical computations and provide the values of various direct and cumulative statistical parameters of interest. These…
We introduce the notion of characteristic function of a quaternionic matrix, whose roots are the left eigenvalues. We prove that for all $2\times 2$ matrices and for $3\times 3$ matrices having some zero entry outside the diagonal there is…
We study the question of the existence of a dual extremal function for a bounded matrix function on the unit circle in connection with the problem of approximation by analytic matrix functions. We characterize the class of matrix functions,…
We introduce a family of discrete analytic functions, called expandable discrete analytic functions, which includes discrete analytic polynomials, and define two products in this family. The first one is defined in a way similar to the…
We analyze matrix convex functions of a fixed order defined on a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus. We obtain for each order conditions for matrix…
we start the study of Schur analysis in the quaternionic setting using the theory of slice hyperholomorphic functions. The novelty of our approach is that slice hyperholomorphic functions allows to write realizations in terms of a suitable…
The present article is an extended version of [6] containing new results and an updated list of references. We review the notion of polar analyticity introduced in a previous paper and succesfully applied in Mellin analysis and quadrature…
Given a collection of test functions, one defines the associated Schur-Agler class as the intersection of the contractive multipliers over the collection of all positive kernels for which each test function is a contractive multiplier. We…
The spectral theory on the S-spectrum was introduced to give an appropriate mathematical setting to quaternionic quantum mechanics, but it was soon realized that there were different applications of this theory, for example, to fractional…
Kernel methods are among the most popular techniques in machine learning. From a frequentist/discriminative perspective they play a central role in regularization theory as they provide a natural choice for the hypotheses space and the…