Banach space
Overview page. Subjects: Mathematics.
A complete normed vector space on the real or complex numbers.
Generality and structures in functional analysis: the influence of Stefan Banach
in The Oxford Handbook of Generality in Mathematics and the Sciences
July 2016; p ublished online July 2017 .
Article. Subjects: Mathematical and Statistical Physics. 15858 words.
This article examines Stefan Banach’s contributions to the field of functional analysis based on the concept of structure and the multiply-flvored expression of generality that arises in...
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THE PME AS AN ABSTRACT EVOLUTION EQUATION. SEMIGROUP APPROACH
in The Porous Medium Equation
October 2006; p ublished online September 2007 .
Chapter. Subjects: Mathematical and Statistical Physics. 14319 words.
This chapter addresses the problem of the construction of solutions of the GPME by viewing it as an abstract evolution equation, or more precisely as an ordinary differential equation with...
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From linear to nonlinear equations, fundamental results
in Numerical Methods for Nonlinear Elliptic Differential Equations
October 2010; p ublished online January 2011 .
Chapter. Subjects: Mathematical and Statistical Physics. 8208 words.
Chapter 1 demonstrates, for the simple mechanical example of a bent rod, the change in character from linear to nonlinear regimes. This is followed by several examples for different types...
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Spectral Theory for Noncommuting Operators
in Feynman's Operational Calculus and Beyond
August 2015; p ublished online September 2015 .
Chapter. Subjects: Mathematical and Statistical Physics; Mathematics. 9320 words.
This chapter, on spectral theory for noncommuting operators, seeks to extend the operational calculus beyond the setting of the analytic functions in the disentangling algebra. When the...
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Disentangling: Definitions, Properties and Elementary Examples
in Feynman's Operational Calculus and Beyond
August 2015; p ublished online September 2015 .
Chapter. Subjects: Mathematical and Statistical Physics; Mathematics. 20736 words.
A rigorous approach to Feynman’s operational calculus, the formation of functions of several noncommuting operators, is introduced, using Feynman’s heuristic “rules” as a guide. Two...
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Disentangling via Tensor Products and Ordered Supports
in Feynman's Operational Calculus and Beyond
August 2015; p ublished online September 2015 .
Chapter. Subjects: Mathematical and Statistical Physics; Mathematics. 20732 words.
More involved types of disentanglings are considered in this chapter. We discuss the situation where the Banach space X can be written as a direct sum X=Y⊕Z, for some Banach spaces Y and Z,...
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Feynman's Operational Calculus and Beyond
August 2015; p ublished online September 2015 .
Book. Subjects: Mathematical and Statistical Physics; Mathematics. 384 pages.
This book provides an abstract theory of Feynman’s operational calculus for functions of (typically) noncommuting operators. Although it is inspired by Feynman’s original heuristic...
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