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## Different aspects of differentiability

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### On isomorphisms of spaces of functional R-shifts for right invertible operators

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Abstract. This paper provides isomorphisms of a space of analytic functions onto spaces of functional R-shifts introduced by the author in [13]. The space contains all functions analytic in a ring {h ∈ ℂ : 0 < |h| < ρ}, 0 < ρ ≤ +∞, do not having an essential singularity at the origin. The results obtained include and extend some of those in the author's works [5], [7].
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• Academy of Agriculture, Nowoursynowska 166, 02-766 Warszawa, Poland
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Bibliografia
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[2] Z. Binderman, On some properties of complex R-shifts, ibid. 25 (1992), 207-217.
[3] Z. Binderman, Some properties of operators of complex differentation and shifts, Scientific Bulletin of Łódź Technical University, Matematyka, 24 (1993), 5-18.
[4] Z. Binderman, Cauchy integral formula induced by right invertible operators, Demonstratio Math. 25 (1992), 671-690.
[5] Z. Binderman, Functional shifts induced by right invertible operators, Math. Nachr. 157 (1992), 211-224.
[6] Z. Binderman, On periodic solutions of equations with right invertible operators induced by functional shifts, Demonstratio Math. 26 (1993), 535-543.
[7] Z. Binderman, A unified approach to shifts induced by right invertible operators, Math. Nachr. 161 (1993), 239-252.
[8] Z. Binderman, On summation formulas induced by functional shifts of right invertible operators, Demonstratio Math. 28 (1995), to appear.
[9] Z. Binderman, Periodic solutions of equations of higher order with a right invertible operator induced by functional shifts, Ann. Univ. M. Curie-Skłodowska 46 (1992), 9-22.
[10] Z. Binderman, On some functional shifts induced by operators of complex differentation, Opuscula Math. 14 (1994), 53-65.
[11] Z. Binderman, Some remarks on sequential shifts induced by right invertible operators, Funct. Approx. 22 (1993), 71-84.
[12] Z. Binderman, Applications of sequential shifts to an interpolation problem, Collect. Math. 44 (1993), 47-57.
[13] Z. Binderman, Some fundamental properties of functional R-shifts for right invertible operators, Comment. Math. 33 (1994), 9-22.
[14] Z. Binderman, A note on functional R-shifts for right invertible operators, Discussiones Math., to appear.
[15] J. B. Miller, The standard summation operator, the Euler-Maclaurin sum formula and the Laplace transformation, J. Austral. Math. Soc. 39 (1985), 376-390.
[16] Nguyen van Mau, Boundary value problems and controllability of linear systems with right invertible operators, Dissertationes Math. 316 (1992).
[17] D. Przeworska-Rolewicz, Shifts and Periodicity for Right Invertible Operators, Research Notes in Math. 43, Pitman Adv. Publ. Program, Boston-London-Melbourne, 1980.
[18] D. Przeworska-Rolewicz, Algebraic Analysis, PWN - Polish Scientific Publishers, and D. Reidel, Warszawa-Dordrecht, 1988.
[19] D. Przeworska-Rolewicz, Spaces of D-paraanalytic elements, Dissertationes Math. 302 (1990).
[20] D. Przeworska-Rolewicz, True shifts, J. Math. Anal. Appl. 170 (1992), 27-48.
[21] D. Przeworska-Rolewicz, Generalized Bernoulli operator and Euler-Maclaurin Formula, in: Advances in Optimization, Proc. 6-th French-German Colloquium on Optimization, Lambrecht, 2-9 June, 1991, Lecture Notes in Econom. and Math. Systems, 382, Springer, Berlin, 1992, 355-368.
[22] D. Przeworska-Rolewicz, The operator exp(hD) and its inverse formula, Demonstratio Math. 26 (1993), 545-552.
[23] H. von Trotha, Structure properties of D-R spaces, Dissertationes Math. 180 (1981).
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DML-PL