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Continuous Functional Calculus
, 2018In this chapter we will introduce by far the most important tool of the theory of operators on Hilbert space, namely functional calculus for self-adjoint operators. We begin with slightly more general considerations focused on normal operators which we will revisit later in Chapter 7.
P. Sołtan
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Pusz–Woronowicz Functional Calculus and Extended Operator Convex Perspectives
Integral equations and operator theory, 2021In this article, we first study, in the framework of operator theory, Pusz and Woronowicz’s functional calculus for pairs of bounded positive operators on Hilbert spaces associated with a homogeneous two-variable function on [0,∞)2\documentclass[12pt ...
F. Hiai, Y. Ueda, Shuhei Wada
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Poly slice monogenic functions, Cauchy formulas and the PS-functional calculus
Journal of operator theory, 2020Since 2006 the theory of slice hyperholomorphic functions and the related spectral theory on the S-spectrum have had a very fast development. This new spectral theory based on the S-spectrum has applications for example in the formulation of quaternionic
D. Alpay +3 more
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An Application of the S-Functional Calculus to Fractional Diffusion Processes
Milan Journal of Mathematics, 2018In this paper we show how the spectral theory based on the notion of S-spectrum allows us to study new classes of fractional diffusion and of fractional evolution processes.
F. Colombo, J. Gantner
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Journal of the London Mathematical Society, 1995
The formula of Helffer and Sjöstrand for functions \(f(H)\) of a selfadjoint operator \(H\) is generalized and put into the real perspective. The author constructs a functional calculus for Banach space operators with real spectra and slowly increasing resolvents when approaching the spectrum.
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The formula of Helffer and Sjöstrand for functions \(f(H)\) of a selfadjoint operator \(H\) is generalized and put into the real perspective. The author constructs a functional calculus for Banach space operators with real spectra and slowly increasing resolvents when approaching the spectrum.
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Quaternionic Functional Calculus
2011The first section of this chapter collects the main results on the theory of slice regular functions. Similarly to what happens in the theory of regular functions in the sense of Cauchy–Fueter, whose results sometimes resemble the analogous results for monogenic functions, also for slice regular functions we have that some statements and their proofs ...
Fabrizio Colombo +2 more
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Functional Calculus for Definitizable Self-adjoint Linear Relations on Krein Spaces
, 2015In the present note a functional calculus $${\phi \mapsto \phi(A)}$$ϕ↦ϕ(A) for self-adjoint definitizable linear relations on Krein spaces is developed.
M. Kaltenbäck, Raphael Pruckner
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Formulations of the -functional calculus and some consequences
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2014In this paper we introduce the two possible formulations of the -functional calculus that are based on the Fueter–Sce mapping theorem in integral form and we introduce the pseudo--resolvent equation.
F. Colombo, J. Gantner
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2010
We extend our functional calculus for a contraction T on \(\mathfrak{K}\) so that certain unbounded functions are also allowed. Let us recall the definitions of the classes \(H^\infty_T\) and \(K^\infty_T\) as given in Secs. 2 and 3 of the preceding chapter: \(H^\infty_T\) consists of the functions \(u\in H^\infty\) ??for which the strong operator ...
Béla Sz.-Nagy +3 more
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We extend our functional calculus for a contraction T on \(\mathfrak{K}\) so that certain unbounded functions are also allowed. Let us recall the definitions of the classes \(H^\infty_T\) and \(K^\infty_T\) as given in Secs. 2 and 3 of the preceding chapter: \(H^\infty_T\) consists of the functions \(u\in H^\infty\) ??for which the strong operator ...
Béla Sz.-Nagy +3 more
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