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A study is made of a symmetric functional calculus for a system of bounded linear operators acting on a Banach space. Finite real linear combinations of the operators have real spectra, but the operators do not necessarily commute with each other. Analytic functions of the operators are formed by using functions taking their values in a Clifford algebra.

The product of relatively regular operators

Jaromír J. Koliha (1975)

Commentationes Mathematicae Universitatis Carolinae

The solution of Kato's conjecture (after Auscher, Hofmann, Lacey, McIntosh and Tchamitchian)

Philippe Tchamitchian (2001)

Journées équations aux dérivées partielles

Kato’s conjecture, stating that the domain of the square root of any accretive operator $L = - div (A \nabla)$ with bounded measurable coefficients in $ℝ^{n}$ is the Sobolev space $H^{1} (ℝ^{n})$ , i.e. the domain of the underlying sesquilinear form, has recently been obtained by Auscher, Hofmann, Lacey, McIntosh and the author. These notes present the result and explain the strategy of proof.

The spectral mapping theorem for one-parameter groups of positive operators on C0(X).

G. Greiner, W. Arendt (1984)

Semigroup forum

The spectral mapping theorem for the essential approximate point spectrum

Christoph Schmoeger (1998)

Colloquium Mathematicae

The Weyl correspondence as a functional calculus

Josefina Alvarez (2000)

Banach Center Publications

The aim of this paper is to use an abstract realization of the Weyl correspondence to define functions of pseudo-differential operators. We consider operators that form a self-adjoint Banach algebra. We construct on this algebra a functional calculus with respect to functions which are defined on the Euclidean space and have a finite number of derivatives.

Théorie spectrale

H. Buchwalter, D. Tarral (1982)

Publications du Département de mathématiques (Lyon)

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The calculus of operator functions and operator convexity [Book]

Currently displaying 1 – 12 of 12