Logarithms and Antilogarithms

Name: Logarithms and Antilogarithms
Author: D. Przeworska-Rolewicz

An Algebraic Analysis Approach

1. Preliminaries. Introduction to Algebraic Analysis.
2. Basic equation. Logarithms and antilogarithms.
3. Logarithms and antilogarithms of higher order.
4. Logarithms and antilogarithms of operators having either finite nullity or finite deficiency.
5. Reduction theorems.
6. Multiplicative case.
7. Leibniz algebras.
8. Linear equations in Leibniz algebras.
9. Trigonometric mappings and elements.
10. Semigroup properties of solutions to linear equations.
11. Operator ehD.
12. Power mappings. Polylogarithmic functions. Nonlinear equations.
13. Smooth logarithms and antilogarithms.
14. Riemann-Hilbert type problems in Leibniz algebras.
15. Periodic problems.
16. Equations with multiplicative involutions of order N.
17. Remarks on the fractional calculus.
Appendix. Functional shifts. By Z. Binderman.
A1. Functions of a right invertible operator.
A2. Functional shifts.
A3. Isomorphisms of spaces of functional shifts.
A4. Functional shifts induced by operators of complex differentiation.
A5. Euler-Maclaurin type formulae.
A6. Differential and integral properties.
References.
Authors Index.
List of Symbols.