Related papers: Functional calculi for sectorial operators and rel…
We prove implicit function theorems for mappings on topological vector spaces over valued fields. In the real and complex cases, we obtain implicit function theorems for mappings from arbitrary (not necessarily locally convex) topological…
In this paper, we utilize various integral representations derived from the Fueter-Sce extension theorem, to introduce novel functional calculi tailored for quaternionic operators of sectorial type. Specifically, due to the different…
Functional integrals are defined in terms of locally compact topological groups and their associated Banach-valued Haar integrals. This approach generalizes the functional integral scheme of Cartier and DeWitt-Morette. The definition allows…
We present an approach to the spectrum and analytic functional calculus for quaternionic linear operators, following the corresponding results concerning the real linear operators. In fact, the construction of the analytic functional…
In the multicentric calculus one takes a polynomial with simple roots as a new global variable and replaces scalar functions {\varphi} by functions f taking values in C^d with d the degree of the polynomial leading to an efficient…
Alesker's theory of generalized valuations unifies smooth measures and constructible functions on real analytic manifolds, extending classical operations on functions and measures. Alesker showed that these operations agree with the…
We obtain new uniqueness theorems for harmonic functions defined on the unit disc or in the half plane. These results are applied to obtain new resolvent descriptions of spectral subspaces of polynomially bounded groups of operators on…
Inspired by the theories of Kaplansky-Hilbert modules and probability theory in vector lattices, we generalise functional analysis by replacing the scalars $\mathbb{R}$ or $\mathbb{C}$ by a real or complex Dedekind complete unital…
Two themes drive this article: identifying the structure necessary to formulate quaternionic operator theory and revealing the relation between complex and quaternionic operator theory. The theory of quaternionic right linear operators is…
A practical solution for the mathematical problem of functional calculus with Laplace-Beltrami operator on surfaces with axial symmetry is found. A quantitative analysis of the spectrum is presented.
A typical approach to analysing statistical properties of expanding maps is to show spectral gaps of associated transfer operators in adapted function spaces. The classical function spaces for this purpose are H\"older spaces and Sobolev…
In this article we give an approach to define continuous functional calculus for bounded quaternionic normal operators defined on a right quaternionic Hilbert space.
We consider a functional calculus for compact operators, acting on the singular values rather than the spectrum, which appears frequently in applied mathematics. Necessary and sufficient conditions for this singular value functional…
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
We consider abstract Banach spaces of analytic functions on general bounded domains that satisfy only a minimum number of axioms. We describe all invertible (equivalently, surjective) weighted composition operators acting on such spaces.…
We present a novel and unifying framework for constructing spectral approximations to fractional integral operators. These spectral approximations are based on transplanted Chebyshev polynomials, which are obtained by composing Chebyshev…
We construct an operational calculus supported on the algebraic operational calculus introduced by Bengochea and Verde. With this operational calculus we study the solution of certain Bessel type equations.
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…
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…
For any non-Archimedean local field $\mathbb{K}$ and any integer $n \geq 1$, we show that the Taibleson operator admits a bounded $\mathrm{H}^\infty(\Sigma_\theta)$ functional calculus on the Bochner space $\mathrm{L}^p(\mathbb{K}^n,Y)$ for…