Variational Analysis

Critical Extremals and Sturmian Extensions

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis
Cover of the book Variational Analysis by Marston Morse, Dover Publications
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Author: Marston Morse ISBN: 9780486153223
Publisher: Dover Publications Publication: February 27, 2013
Imprint: Dover Publications Language: English
Author: Marston Morse
ISBN: 9780486153223
Publisher: Dover Publications
Publication: February 27, 2013
Imprint: Dover Publications
Language: English

This text presents extended separation, comparison, and oscillation theorems that replace the classical analysis of Legendre, Jacobi, Hilbert, and others. Its analysis of related quadratic functionals shows how critical extremals can substitute for minimizing extremals.
Author Marston Morse is renowned for his development of a version of variational theory with applications to equilibrium problems in mathematical physics—the theory known as Morse theory, which forms a vital role in global analysis. He begins this treatment of variational analysis with an extended investigation of critical extremals that proceeds to quadratic index forms, advanced and free. Additional topics include focal conditions and Sturm-like theorems, general boundary conditions, and prestructures for characteristic root theory. A helpful pair of appendixes include supplementary information on free linear conditions and subordinate quadratic forms and their complementary forms.

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This text presents extended separation, comparison, and oscillation theorems that replace the classical analysis of Legendre, Jacobi, Hilbert, and others. Its analysis of related quadratic functionals shows how critical extremals can substitute for minimizing extremals.
Author Marston Morse is renowned for his development of a version of variational theory with applications to equilibrium problems in mathematical physics—the theory known as Morse theory, which forms a vital role in global analysis. He begins this treatment of variational analysis with an extended investigation of critical extremals that proceeds to quadratic index forms, advanced and free. Additional topics include focal conditions and Sturm-like theorems, general boundary conditions, and prestructures for characteristic root theory. A helpful pair of appendixes include supplementary information on free linear conditions and subordinate quadratic forms and their complementary forms.

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