Generalized sturm separation theorem

• Autorzy: Przeworska-Rolewicz D.
• Języki publikacji: EN

Abstrakty

EN

True shifts for right invertible operators has been examined in several papers in various aspects (cf. PR[4], PR[5]). A generalization of Sturm separation theorem was given in PR[2] in the case when a right invertible operator under consideration had the one-dimensional kernel. Following the preprint [6], it is shown that the Sturm theorem holds without any assumption about the dimension of that kernel. In the last section of the present paper there are considered the multiplicative symbols in Leibniz algebras.

Słowa kluczowe

EN

Leibniz algebra; hypercyclic operator; periodic operator; periodic element; oscillatory element; symbol function

PL

operatory; algebra Leibniza; funkcje symboliczne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2003
• Tom: Vol. 36, nr 3
• Strony: 735--746
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Przeworska-Rolewicz D.

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland

Bibliografia

• BPR[1] Z. Binderman and D. Przeworska-Rolewicz, Almost quasinilpotent right inverses. In: Proc. Intern. Conf. Different Aspects of Differentiability II. Warszawa, September 1995. Integral Transforms and Special Functions 1-2, 4 (1996), 23-38.
• C[1] W. A. Coppel, Disconjugacy. Lecture Notes in Mathematics, Springer-Verlag, Berlin-Heidelberg-New York, 1971.
• PR[1] D. Przeworska-Rolewicz, Algebraic Analysis, PWN-Polish Scientific Publishers and D. Reidel, Warszawa-Dordrecht, 1988.
• PR[2] D. Przeworska-Rolewicz, Advantages of one-dimensional kernels, Math. Nachrichten 149 (1990), 133-147.
• PR[3] D. Przeworska-Rolewicz, A priori determined solutions of linear equations, Math. Japonica 2, 44 (1996), 395-412.
• PR[4] D. Przeworska-Rolewicz, Logarithms and Antüogarithms. An Algebraic Analysis Approach, With Appendix by Z. Binderman. Kluwer Academic Publishers, Dordrecht, 1998.
• PR[5] D. Przeworska-Rolewicz, True shifts revisited, Demonstratio Math. 34, 1 (2001), 111-122.
• PR[6] D. Przeworska-Rolewicz, Generalized Strurm separation theorem, Preprint IM PAN N° 625, Warszawa, April 2002.
• R[1] S. Rolewicz, On orbits of elements, Studia Math. 32 (1969), 17-22.
• S[1] J. H. Shapiro, Composition Operators and Classical Function Theory, Springer-Verlag, New York, 1993.
• T[1] H. von Trotha, Structure Properties of D-R Spaces, Dissertationes Math. 180, Warszawa, 1981.