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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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Differential Calculus of Zeon Functions
Advances in Applied Clifford Algebras, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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.
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Mehler’s formula and functional calculus
Science China Mathematics, 2019Several formulas involving the quantization of singular Hamiltonians are derived by the use of Mehler's formula. Three appendices serve as relevant source for background material. In the first section, the Weyl quantization of \(F(x^2 + \xi^2)\) is calculated explicitly, when \(F\) is of the Schwartz class in one dimension.
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Functional Differential Calculus of Operators
Journal of Mathematical Physics, 1964The functional derivative with respect to operators of operator functionals is defined for operators which satisfy certain commutation relations of interest in quantum field theory. From this definition, a functional differential calculus is developed for functionals of tensor as well as spinor fields.
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Feynman’s Functional Calculus and Stochastic Calculus of Variations
1991The mathematical structure of Quantum Mechanics is usually introduced as a calculus of non-commuting self-adjoint (unbounded) operators, the “observables,” on a Hilbert space of “states” (cf. [15]). There is no doubt that Quantum Mechanics is consistent and describes correctly many experiments, but we are supposed to renounce completely the ...
Ana Bela Cruzeiro, Jean Claude Zambrini
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Axially Harmonic Functions and the Harmonic Functional Calculus on the S-spectrum
Journal of Geometric Analysis, 2022Antonino De Martino, Irene Sabadini
exaly