On the Foundations of Nonlinear Generalized Functions I and II is popular PDF and ePub book, written by Michael Grosser in 2001, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, On the Foundations of Nonlinear Generalized Functions I and II can be Read Online from any device for your convenience.
On the Foundations of Nonlinear Generalized Functions I and II Book PDF Summary
In part 1 we construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential calculus in infinite dimensional (convenient) vector spaces, previous attempts in this direction are unified and completed. Several classification results are achieved and applications to nonlinear differential equations involving singularities are given. Part 2 gives a comprehensive analysis of algebras of Colombeau-type generalized functions in the range between the diffeomorphism-invariant quotient algebra ${\mathcal G}^d = {\mathcal E}_M/{\mathcal N}$ introduced in part 1 and Colombeau's original algebra ${\mathcal G}^e$.Three main results are established: first, a simple criterion describing membership in ${\mathcal N}$ (applicable to all types of Colombeau algebras) is given; second, two counterexamples demonstrate that ${\mathcal G}^d$ is not injectively included in ${\mathcal G}^e$; and finally, it is shown that in the range ""between"" ${\mathcal G}^d$ and ${\mathcal G}^e$ only one more construction leads to a diffeomorphism invariant algebra. In analyzing the latter, several classification results essential for obtaining an intrinsic description of ${\mathcal G}^d$ on manifolds are derived.
Detail Book of On the Foundations of Nonlinear Generalized Functions I and II PDF
- Author : Michael Grosser
- Release : 03 July 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821827291
- Genre : Mathematics
- Total Page : 93 pages
- Language : English
- PDF File Size : 21,8 Mb
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