Logarithms and Antilogarithms: An Algebraic Analysis Approach by D. Przeworska-Rolewicz
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Logarithms and Antilogarithms
Logarithms and Antilogarithms
Summary
Proposes and explores a definition of logarithmic mappings as invertible selectors of multifunctions induced by linear operators with domains and ranges in an algebra over a field of characteristic zero. This volume is intended for research mathematicians and other scientists of other disciplines whose work involves the solution of equations.
Logarithms and Antilogarithms Summary
Table of Contents
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.
Additional information
NPB9780792349747
9780792349747
0792349741
Logarithms and Antilogarithms: An Algebraic Analysis Approach by D. Przeworska-Rolewicz
New
Hardback
Springer
1998-03-31
357
N/A
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