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1	Topics on Mean Value Theorems Huang, Gen-Ben 19 January 2001 (has links) Please read the PDF file of my thesis. accumulation point differential mean value theorem
2	Koliha–Drazin invertibles form a regularity Smit, Joukje Anneke 10 1900 (has links) The axiomatic theory of ` Zelazko defines a variety of general spectra where specified axioms are satisfied. However, there arise a number of spectra, usually defined for a single element of a Banach algebra, that are not covered by the axiomatic theory of ` Zelazko. V. Kordula and V. M¨uller addressed this issue and created the theory of regularities. Their unique idea was to describe the underlying set of elements on which the spectrum is defined. The axioms of a regularity provide important consequences. We prove that the set of Koliha-Drazin invertible elements, which includes the Drazin invertible elements, forms a regularity. The properties of the spectrum corresponding to a regularity are also investigated. / Mathematical Sciences / M. Sc. (Mathematics) Banach algebra Radical Spectrum Resolvent Quasinilpotent Nilpotent Spectral idempotent Isolated spectral point Accumulation point Regularity Koliha-Drazin invertible Quasipolar KD-spectrum D-spectrum Laurent expansion Poles of the resolvent 511.322 Axiomatic set theory Banach algebras Spectrum analysis Spectral sequences (Mathematics)
3	Koliha–Drazin invertibles form a regularity Smit, Joukje Anneke 10 1900 (has links) The axiomatic theory of ` Zelazko defines a variety of general spectra where specified axioms are satisfied. However, there arise a number of spectra, usually defined for a single element of a Banach algebra, that are not covered by the axiomatic theory of ` Zelazko. V. Kordula and V. M¨uller addressed this issue and created the theory of regularities. Their unique idea was to describe the underlying set of elements on which the spectrum is defined. The axioms of a regularity provide important consequences. We prove that the set of Koliha-Drazin invertible elements, which includes the Drazin invertible elements, forms a regularity. The properties of the spectrum corresponding to a regularity are also investigated. / Mathematical Sciences / M. Sc. (Mathematics) Banach algebra Radical Spectrum Resolvent Quasinilpotent Nilpotent Spectral idempotent Isolated spectral point Accumulation point Regularity Koliha-Drazin invertible Quasipolar KD-spectrum D-spectrum Laurent expansion Poles of the resolvent 511.322 Axiomatic set theory Banach algebras Spectrum analysis Spectral sequences (Mathematics)

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