Differential Equations with Involutions

Nonfiction, Science & Nature, Mathematics, Differential Equations, Science, Physics, Mathematical Physics
Cover of the book Differential Equations with Involutions by Alberto Cabada, F. Adrián F. Tojo, Atlantis Press
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Author: Alberto Cabada, F. Adrián F. Tojo ISBN: 9789462391215
Publisher: Atlantis Press Publication: January 6, 2016
Imprint: Atlantis Press Language: English
Author: Alberto Cabada, F. Adrián F. Tojo
ISBN: 9789462391215
Publisher: Atlantis Press
Publication: January 6, 2016
Imprint: Atlantis Press
Language: English

This monograph covers the existing results regarding Green’s functions for differential equations with involutions (DEI).The first part of the book is devoted to the study of the most useful aspects of involutions from an analytical point of view and the associated algebras of differential operators. The work combines the state of the art regarding the existence and uniqueness results for DEI and new theorems describing how to obtain Green’s functions, proving that the theory can be extended to operators (not necessarily involutions) of a similar nature, such as the Hilbert transform or projections, due to their analogous algebraic properties. Obtaining a Green’s function for these operators leads to new results on the qualitative properties of the solutions, in particular maximum and antimaximum principles.

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This monograph covers the existing results regarding Green’s functions for differential equations with involutions (DEI).The first part of the book is devoted to the study of the most useful aspects of involutions from an analytical point of view and the associated algebras of differential operators. The work combines the state of the art regarding the existence and uniqueness results for DEI and new theorems describing how to obtain Green’s functions, proving that the theory can be extended to operators (not necessarily involutions) of a similar nature, such as the Hilbert transform or projections, due to their analogous algebraic properties. Obtaining a Green’s function for these operators leads to new results on the qualitative properties of the solutions, in particular maximum and antimaximum principles.

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