Related papers: Functional Calculus for definitizable self-adjoint…
The multidimensional functional calculus of semigroup generators, based on the class of Bernstein functions in several variables is developed, the spectral mapping theorems for joint spectra have been stated, the condition for holomorphy of…
In this paper, a spectral theorem is proved for self-adjoint cyclically compact partial integral operators in the space of functions with mixed norm, which is a Kaplansky--Hilbert module. The decomposition through eigenfunctions, integral…
We establish an eigenfunctional theorem for positive operators, evocative of the Krein--Rutman theorem. A more general version gives a joint eigenfunctional for commuting operators.
The abstract theory of self-adjoint extensions of symmetric operators is used to construct self-adjoint realizations of a second-order elliptic operator on $\mathbb{R}^{n}$ with linear boundary conditions on (a relatively open part of) a…
In 2016, the spectral theory on the $S$-spectrum was used to establish the $H^\infty$-functional calculus for quaternionic or Clifford operators. This calculus applies for example to sectorial or bisectorial right linear operators $T$ and…
The article deals with iterative methods of solving linear operator equations $x = Bx + f$ and $Ax = f$ with self-adjoint operators in Hilbert space $X$ in critical case when $\rho(B) = 1$ and $0 \in {\rm Sp}\, A$. The main results are…
The main result of the paper is a description of the class of functions on the unit circle, for which Krein's trace formula holds for arbitrary pairs of unitary operators with trace class difference. We prove that this class of functions…
Let $H_0$ and $H$ be self-adjoint operators in a Hilbert space. In the scattering theory framework, we describe the essential spectrum of the difference $\varphi(H)-\varphi(H_0)$ for piecewise continuous functions $\varphi$. This…
This paper presents a general study of one-dimensional differentiability for functionals defined on convex domains that are not necessarily open. The local approximation is carried out using affine functionals, as opposed to linear…
In this paper, we give the definitions of the non-self-adjoint spectral triple and its spectral Einstein functional. We compute the spectral Einstein functional associated with the nonminimal de Rham-Hodge operator on even-dimensional…
Ext-int.\ one affine functions are functions affine in the direction of one-divisible exterior forms, with respect to exterior product in one variable and with respect to interior product in the other. The purpose of this article is to…
In this paper, we shall consider the notion of bicomplex inner product and define bicomplex Hilbert space. We shall define $L^{2}[a,b]$ where the functions take bicomplex values. We shall prove the Theorem for a bounded self adjoint…
Regarding quaternions as normal matrices, we first characterize the $2\times 2$ matrix-valued functions, defined on subsets of quaternions, whose values are quaternions. Then we investigate the regularity of quaternionic-valued functions,…
Isomorphisms of separable Hilbert spaces are analogous to isomorphisms of n-dimensional vector spaces. However, while n-dimensional spaces in applications are always realized as the Euclidean space R^n, Hilbert spaces admit various useful…
We produce a simple criterion and a constructive recipe to identify those self-adjoint extensions of a lower semi-bounded symmetric operator on Hilbert space which have the same lower bound as the Friedrichs extension. Applications of this…
In this paper, the \lambda\phi^4 scalar feld effective action, in the one-loop approximation, is calculated by using the Krein space quantization. We show that the effective action is naturally fnite and the singularity does not appear in…
In this work, generalizations of some inequalities for continuous $h$-synchronous ($h$-asynchronous) functions of linear bounded selfadjoint operators under positive linear maps in Hilbert spaces are proved.
Sufficient and necessary conditions on the spectral measure of a self-adjoint operator $A$, acting in a Hilbert space, are obtained, under which for any continuous scalar function the operator function $\phi(A+\gamma B)$ is holomorphic with…
This paper gives the pointwise H\"older (or multifractal) spectrum of continuous functions on the interval $[0,1]$ whose graph is the attractor of an iterated function system consisting of $r\geq 2$ affine maps on $\mathbb{R}^2$. These…
In this paper we develop the functional calculus for elliptic operators on compact Lie groups without the assumption that the operator is a classical pseudo-differential operator. Consequently, we provide a symbolic descriptions of complex…