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Logarithmic and antilogarithmic mappings

Seria
Rozprawy Matematyczne tom/nr w serii: 337 wydano: 1994
Zawartość
Warianty tytułu
Abstrakty
EN

CONTENTS
Introduction............................................................................................................................................5
0. Preliminaries.......................................................................................................................................6
1. Basic equation. Logarithms and antilogarithms..................................................................................8
2. Logarithms and antilogarithms of higher order.................................................................................19
3. Reduction theorems..........................................................................................................................24
4. Multiplicative case.............................................................................................................................36
5. Leibniz case.......................................................................................................................................41
6. Exponential, power and polylogarithmic functions.............................................................................51
7. Complex case....................................................................................................................................57
8. Smooth logarithms and antilogarithms..............................................................................................64
9. Logarithmic and antilogarithmic mappings induced by left invertible and invertible operators...........70
10. Other generalizations.......................................................................................................................82
   References...........................................................................................................86
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 337
Liczba stron
87
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCXXXVII
Daty
wydano
1994
otrzymano
1993-04-30
poprawiono
1994-04-19
Twórcy
  • Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland
Bibliografia
  • Z. Binderman [1], Functional shifts induced by right invertible operators, Math. Nachr. 157 (1992), 211-224.
  • Z. Binderman [2], A unified approach to shifts induced by right invertible operators, Math. Nachr. 161 (1993), 239-252.
  • J. B. Conway and B. B. Morrel [1], Roots and logarithms of bounded operators on a Hilbert space, J. Funct. Anal. 70 (1987),171-193.
  • Z. Dudek [1], On decompositions of quasi-Leibniz D-R algebras, Demonstratio Math. 14 (1981), 745-757.
  • Z. Dudek [2], On multiplicative operators in commutative algebras, Demonstratio Math. 23 (1990), 921-928.
  • C. G. Fraser [1], The calculus of algebraic analysis: some observations on mathematical analysis in the 18th century, Arch. Hist. Exact Sci. 39 (1988), 317-335.
  • H. Kornacki [1], Non-Leibniz components in non-commutative algebras with unit, Demonstratio Math. 18 (1986), 483-497.
  • M. Kuczma [1], An Introduction to the Theory of Functional Equations and Inequalities. Cauchy's Equation and Jensen's Equation, PWN-Polish Scientific Publishers and the Silesian University, Warszawa-Kraków-Katowice, 1985.
  • H. Lausch and D. Przeworska-Rolewicz [1], Pseudocategories, paraalgebras and linear operators, Math. Nachr. 138 (1988), 67-87.
  • H. Lausch and D. Przeworska-Rolewicz [2], Some functional equations appearing in Algebraic Analysis, Opuscula Math. 6 (1990), 111-122.
  • S. J. Lee and M. Z. Nashed [1], Algebraic and topological selections of multi-valued linear relations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 17 (1990), 111-126.
  • D. E. Loeb and G.-C. Rota [1], Formal power series of logarithmic type, Adv. Math. 75 (1989), 1-118.
  • J. B. Miller [1], The standard summation operator, the Euler-Maclaurin sum formula and the Laplace transformation, J. Austral. Math. Soc. 39 (1985), 376-390.
  • Nguyen Van Mau [1], Generalized algebraic elements and singular integral equations with transformed arguments, Wydawnictwa Politechniki Warszawskiej (Warsaw University of Technology Publications), Warszawa, 1989.
  • Nguyen Van Mau [2], Boundary value problems and controllability of linear systems with right invertible operators, Dissertationes Math. 316 (1992).
  • D. Przeworska-Rolewicz [1], Algebraic Analysis, PWN-Polish Scientific Publishers and D. Reidel, Warszawa-Dordrecht, 1988.
  • D. Przeworska-Rolewicz [2], Spaces of D-paraanalytic elements, Dissertationes Math. 302 (1990).
  • D. Przeworska-Rolewicz [3], Advances of one-dimensional kernels, Math. Nachr. 149 (1990), 133-147.
  • D. Przeworska-Rolewicz [4], Commutators with right invertible operators, J. Math. Anal. Appl. 158 (1991), 414-426.
  • D. Przeworska-Rolewicz [5], True shifts, J. Math. Anal. Appl. 170 (1992), 27-48.
  • D. Przeworska-Rolewicz [6], Generalized Bernoulli operator and Euler-Maclaurin formula, in: Advances of Optimization, Proc. 6-th French-German Conference on Optimization, Lambrecht (FRG), 2-8 June 1991, Lecture Notes in Econom. and Math. Systems 382, Springer, Berlin, 1992, 355-368.
  • D. Przeworska-Rolewicz [7], The operator exp(hD) and its inverse formula, Demonstratio Math. 26 (1993), 545-552.
  • D. Przeworska-Rolewicz [8], D-algebras with logarithms, Math. Nachr. 161 (1993), 321-344.
  • D. Przeworska-Rolewicz [9], On logarithmic and antilogarithmic mappings induced by right invertible operators, 1. Real case, preprint no. 508, Institute of Mathematics, Polish Acad. Sci., Warszawa, 1993.
  • D. Przeworska-Rolewicz and S. Rolewicz [1], Equations in Linear Spaces, PWN-Polish Scientific Publishers, Warszawa, 1968.
  • D. Przeworska-Rolewicz and H. von Trotha [1], Right inverses in D-R algebras with unit, J. Integral Equations 3 (1981), 245-259.
  • G. I. Targonski [1], Seminar on Functional Operators and Equations, Lecture Notes in Math. 33, Springer, Berlin, 1967.
  • G. Virsik [1], Right inverses of vector fields, Analysis Paper 84, Dept. of Math., Monash University, Clayton (Melbourne), November 1992.
  • D. Zagier [1], The Bloch-Wigner-Ramakrishnan polylogarithm function, Math. Ann. 286 (1990), 613-624.
Języki publikacji
EN
Uwagi
1991 Mathematics Subject Classification: 47C05, 47H17, 47S10, 33B10.
Identyfikator YADDA
bwmeta1.element.zamlynska-ba01965e-01ed-4379-901a-51724be64112
Identyfikatory
ISSN
0012-3862
Kolekcja
DML-PL
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