Mukhopadhyay Higher Order Derivatives

Erscheinungsjahr 2012
ISBN: 978-1-4398-8048-7
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 220 Seiten

Reihe: Monographs and Surveys in Pure and Applied Mathematics

The concept of higher order derivatives is useful in many branches of mathematics and its applications. As they are useful in many places, nth order derivatives are often defined directly. Higher Order Derivatives discusses these derivatives, their uses, and the relations among them. It covers higher order generalized derivatives, including the Peano, d.l.V.P., and Abel derivatives; along with the symmetric and unsymmetric Riemann, Cesàro, Borel, LP-, and Laplace derivatives.

Although much work has been done on the Peano and de la Vallée Poussin derivatives, there is a large amount of work to be done on the other higher order derivatives as their properties remain often virtually unexplored. This book introduces newcomers interested in the field of higher order derivatives to the present state of knowledge. Basic advanced real analysis is the only required background, and, although the special Denjoy integral has been used, knowledge of the Lebesgue integral should suffice.

Zielgruppe

Mathematicians in real analysis and differential equations.

Autoren/Hrsg.

Mukhopadhyay, Satya

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

Introduction
Higher order derivatives
Divided difference of order n
General derivatives of order n
Generalized Riemann derivatives of order n
Peano derivatives
Riemann* derivatives
Symmetric de la Vallée Poussin derivatives
Symmetric Riemann* derivatives
Cesàro derivatives
Symmetric Cesàro derivatives
Borel derivatives
Symmetric Borel derivatives
Lp-derivatives
Symmetric Lp-derivatives
Abel derivatives
Laplace derivatives
Symmetric Laplace derivatives

Relations between derivatives
Ordinary and Peano derivatives
Riemann* and Peano derivatives
Symmetric Riemann* and symmetric de la Vallée Poussin derivatives
Cesàro and Peano derivatives
Peano and symmetric de la Vallée Poussin derivatives and smoothness of order k
Symmetric Cesàro and symmetric de la Vallée Poussin derivatives
Borel and Peano derivatives
Symmetric Borel and symmetric de la Vallée Poussin derivatives
Borel and symmetric Borel derivatives and Borel smoothness of order k
Peano and Lp-derivatives
Lp- and symmetric Lp-derivatives
Symmetric de la Vallée Poussin and symmetric Lp-derivatives
Borel and Lp-derivatives
Symmetric Borel and symmetric Lp-derivatives
Cesàro and Borel derivatives
Symmetric Cesàro and symmetric Borel derivatives
Abel and symmetric de la Vallée Poussin derivatives
Laplace, Peano and generalized Peano derivatives
Laplace and Borel derivatives
Symmetric Laplace and symmetric de la Vallée Poussin derivatives
Laplace and symmetric Laplace derivatives
Peano and the unsymmetric Riemann derivatives
Symmetric de la Vallée Poussin and the symmetric Riemann derivatives
Generalized Riemann and Peano derivatives
MZ- and Peano derivatives