Integral formulae for special cases of Taylor's functional calculus

• Autorzy: D. W. Albrecht
• Języki publikacji: EN

Abstrakty

EN

In this paper integral formulae, based on Taylor's functional calculus for several operators, are found. Special cases of these formulae include those of Vasilescu and Janas, and an integral formula for commuting operators with real spectra.

Kategorie tematyczne

• 47A56: Functions whose values are linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones)
• 47A60: Functional calculus

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1993
• Tom: 105
• Numer: 1
• Strony: 51-68

Daty

wydano

1993

otrzymano

1991-12-17

poprawiono

1993-02-03

Twórcy

autor

D. W. Albrecht

• Mathematics Department, Monash University Clayton, Victoria 3168, Australia

Bibliografia

• [1] D. W. Albrecht, Matrix techniques in the study of complexes, Analysis Paper 79, Monash University, Clayton, Victoria, 1991.
• [2] R. Arens, Analytic-functional calculus in commutative topological algebras, Pacific J. Math. 11 (1961), 405-429.
• [3] I. Colojoară and C. Foiaş, Theory of Generalized Spectral Operators, Math. Appl. 9, Gordon and Breach, New York 1968.
• [4] G. M. Henkin, Integral representations of functions holomorphic in strictly pseudoconvex domains and some applications, Mat. Sb. 78 (1969), 611-632 (in Russian).
• [5] J. Janas, On integral formulas and their applications in functional calculus, J. Math. Anal. Appl. 114 (1986), 328-339.
• [6] S. Lang, Algebra, Addison-Wesley, 1965.
• [7] A. McIntosh, A. Pryde and W. Ricker, Comparison of joint spectra for certain classes of commuting operators, Macquarie Math. Reports (1986), 86-0069.
• [8] R. M. Range, Holomorphic Functions and Integral Representations in Several Complex Variables, Springer, New York 1986.
• [9] J. L. Taylor, A joint spectrum for several commuting operators, J. Funct. Anal. 6 (1970), 172-191.
• [10] J. L. Taylor, Analytic-functional calculus for several commuting operators, Acta Math. 125 (1970), 1-38.
• [11] F. H. Vasilescu, A Martinelli type formula for the analytic functional calculus, Rev. Roumaine Math. Pures Appl. 23 (10) (1978), 1587-1605.
• [12] V. S. Vladimirov, Methods of the Theory of Functions of Several Complex Variables, Nauka, Moscow 1964; English transl.: M.I.T. Press, Cambridge, Mass., 1966.