Nova Publishers
My Account Nova Publishers Shopping Cart
HomeBooksSeriesJournalsReference CollectionseBooksInformationSalesImprintsFor Authors
  Top » Catalog » Books » My Account  |  Cart Contents  |  Checkout   
Quick Find
Use keywords to find the product you are looking for.
Advanced Search
What's New? more
Doxycycline: Medical Uses and Effects
Shopping Cart more
0 items
Shipping & Returns
Privacy Notice
Conditions of Use
Contact Us
Notifications more
NotificationsNotify me of updates to Quasi-Invariant and Pseudo-Differentiable Measures in Banach Spaces
Tell A Friend
Tell someone you know about this product.
Quasi-Invariant and Pseudo-Differentiable Measures in Banach Spaces
Retail Price: $215.00
10% Online Discount
You Pay:

Authors: Sergey Ludkovsky (Dept. of Applied Mathematics, Moscow State Technical Univ., MIREA, Moscow, Russia) 
Book Description:
This book is devoted to new results of investigations of non-Archimedean functional analysis, which is becoming more important nowadays due to the development of non-Archimedean mathematical physics, particularly, quantum mechanics, quantum field theory, theory of super-strings and super-gravity (VV89, VVZ94, ADV88, Cas02, DD00, Ish84, Khr90, Lud99t, Lud03b, Mil84, Jan 98). Recently non-Archimedean analysis was found to be useful in dynamical systems, mathematical biology, mathematical psychology, cryptology and information theory. On the other hand, quantum mechanics is based on measure theory and probability theory. The results of this
book published mainly in papers [Lud02a, Lud03s2, Lud04a, Lud96c, Lud99a, Lud00a, Lud99t, Lud01f, Lud00f, Lud99s, Lud04b] have served for investigations of non-Archimedean stochastic processes (Lud0321, Lud0341, Lud0348,Lud01f, LK02). Stochastic approach in quantum-field theory is actively used and investigated especially in recent years (see, for example, and references therein (AHKMT93, AHKT84]). As it is well-known in the theory of functions great role is played by continuous functions and differentiable functions.
In classical measure theory, the analog of continuity is quasi-invariance relative to shifts and actions of linear or non-linear operators in the Banach space. Moreover, differentiability of measures is the stronger condition and there is a very large theory about it in the classical case. Apart from it, the non-Archimedean case was less studied. Since there are not any non-trivial differentiable functions from the p-adic field Qp into R or into another p-adic non-Archimedean field Qp' with p not equal to p', then instead of differentiability of measures their pseudo-differentiability is considered.
Traditional or classical mathematical analysis and functional analysis work mainly over the real and complex fields. But there are well-known many other infinite fields with non-trivial multiplicative norms since the end of the 19-th century and is called the non-Archimedean norm. Such fields and vector spaces with non-Archimedean norms are frequently called for short non-Archimedean fields and non-Archimedean normed spaces correspondingly. Therefore, mathematical analysis and functional analysis over non-Archimedean fields have developed already during a rather long period of time, but they remain substantially less elaborated in comparison with classical ones

We’ve partnered with Copyright Clearance Center to make it easy for you to request permissions to reuse Nova content.
For more information, click here or click the "Get Permission" button below to link directly to this book on Copyright Clearance Center's website.

Table of Contents:



1. Real-valued measures, pp.1
1.1 Introduction, pp. 1
1.2 Distributions and families of measures, pp. 3
1.3 Quasi-invariant measures, pp. 28
1.4 Pseudo-differentiable measures, pp. 57
1.5 Convergence of measures, pp. 67
1.6 Measures with particular properties, pp. 73
1.7 Comments, pp. 86

2. Non-Archimedean valued measures, pp. 91
2.1 Introduction, pp. 91
2.2 Non-Archimedean valued distributions, pp. 92
2.3 Quasi-invariant Ks-valued measures, pp. 109
2.4 Pseudo-differentiable Ks-valued measures, pp. 121
2.5 Convergence of Ks-valued measures, pp. 124
2.6 Measures with particular properties, pp. 128
2.7 Comments, pp. 140

3. Algebras of real measures on groups, pp. 143
3.1 Introduction, pp. 143
3.2 Algebras of measures and functions, pp. 143
3.3 Commentspp, pp. 152

4. Algebras of non-Archimedean measures on groups, pp. 153
4.1 Introduction, pp. 153
4.2 Algebras of measures and functions, pp. 153
4.3 Comments, pp. 162

A. Operators in Banach spaces, pp. 173

B. Non-Archimedean polyhedral expansions, pp. 179
B.1 Ultra-uniform spaces, pp. 179
B.2 Polyhedral expansions, pp. 184



      Mathematics Research Developments
   Binding: Hardcover
   Pub. Date: 2009
   Pages: 7 x 10, 198 pp
   ISBN: 978-1-60692-734-2
   Status: AV
Status Code Description
AN Announcing
FM Formatting
PP Page Proofs
FP Final Production
EP Editorial Production
PR At Prepress
AP At Press
AV Available
Customers who bought this product also purchased
Special Education in the 21st Century
Special Education in the 21st Century
Electric Vehicles: Technology, Research and Development
Electric Vehicles: Technology, Research and Development
Sovereign Wealth Funds
Sovereign Wealth Funds
Hazardous Waste: Classifications and Treatment Technologies
Hazardous Waste: Classifications and Treatment Technologies
The Chemistry and Mathematics of DNA Polyhedra
The Chemistry and Mathematics of DNA Polyhedra
Fire Safety
Fire Safety
Special Focus Titles
01.Violent Communication and Bullying in Early Childhood Education
02.Cultural Considerations in Intervention with Women and Children Exposed to Intimate Partner Violence
03.Chronic Disease and Disability: The Pediatric Lung
04.Fruit and Vegetable Consumption and Health: New Research
05.Fire and the Sword: Understanding the Impact and Challenge of Organized Islamism. Volume 2

Nova Science Publishers
© Copyright 2004 - 2021

Quasi-Invariant and Pseudo-Differentiable Measures in Banach Spaces