Non-Self-Adjoint Boundary Eigenvalue Problems

Nonfiction, Science & Nature, Mathematics, Differential Equations, Mathematical Analysis
Cover of the book Non-Self-Adjoint Boundary Eigenvalue Problems by R. Mennicken, M. Möller, Elsevier Science
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: R. Mennicken, M. Möller ISBN: 9780080537733
Publisher: Elsevier Science Publication: June 26, 2003
Imprint: North Holland Language: English
Author: R. Mennicken, M. Möller
ISBN: 9780080537733
Publisher: Elsevier Science
Publication: June 26, 2003
Imprint: North Holland
Language: English

This monograph provides a comprehensive treatment of expansion theorems for regular systems of first order differential equations and n-th order ordinary differential equations.
In 10 chapters and one appendix, it provides a comprehensive treatment from abstract foundations to applications in physics and engineering. The focus is on non-self-adjoint problems. Bounded operators are associated to these problems, and Chapter 1 provides an in depth investigation of eigenfunctions and associated functions for bounded Fredholm valued operators in Banach spaces. Since every n-th order differential equation is equivalent
to a first order system, the main techniques are developed for systems. Asymptotic fundamental
systems are derived for a large class of systems of differential equations. Together with boundary
conditions, which may depend polynomially on the eigenvalue parameter, this leads to the definition of Birkhoff and Stone regular eigenvalue problems. An effort is made to make the conditions relatively easy verifiable; this is illustrated with several applications in chapter 10.
The contour integral method and estimates of the resolvent are used to prove expansion theorems.
For Stone regular problems, not all functions are expandable, and again relatively easy verifiable
conditions are given, in terms of auxiliary boundary conditions, for functions to be expandable.
Chapter 10 deals exclusively with applications; in nine sections, various concrete problems such as
the Orr-Sommerfeld equation, control of multiple beams, and an example from meteorology are investigated.

Key features:

• Expansion Theorems for Ordinary Differential Equations
• Discusses Applications to Problems from Physics and Engineering
• Thorough Investigation of Asymptotic Fundamental Matrices and Systems
• Provides a Comprehensive Treatment
• Uses the Contour Integral Method
• Represents the Problems as Bounded Operators
• Investigates Canonical Systems of Eigen- and Associated Vectors for Operator Functions

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

This monograph provides a comprehensive treatment of expansion theorems for regular systems of first order differential equations and n-th order ordinary differential equations.
In 10 chapters and one appendix, it provides a comprehensive treatment from abstract foundations to applications in physics and engineering. The focus is on non-self-adjoint problems. Bounded operators are associated to these problems, and Chapter 1 provides an in depth investigation of eigenfunctions and associated functions for bounded Fredholm valued operators in Banach spaces. Since every n-th order differential equation is equivalent
to a first order system, the main techniques are developed for systems. Asymptotic fundamental
systems are derived for a large class of systems of differential equations. Together with boundary
conditions, which may depend polynomially on the eigenvalue parameter, this leads to the definition of Birkhoff and Stone regular eigenvalue problems. An effort is made to make the conditions relatively easy verifiable; this is illustrated with several applications in chapter 10.
The contour integral method and estimates of the resolvent are used to prove expansion theorems.
For Stone regular problems, not all functions are expandable, and again relatively easy verifiable
conditions are given, in terms of auxiliary boundary conditions, for functions to be expandable.
Chapter 10 deals exclusively with applications; in nine sections, various concrete problems such as
the Orr-Sommerfeld equation, control of multiple beams, and an example from meteorology are investigated.

Key features:

• Expansion Theorems for Ordinary Differential Equations
• Discusses Applications to Problems from Physics and Engineering
• Thorough Investigation of Asymptotic Fundamental Matrices and Systems
• Provides a Comprehensive Treatment
• Uses the Contour Integral Method
• Represents the Problems as Bounded Operators
• Investigates Canonical Systems of Eigen- and Associated Vectors for Operator Functions

More books from Elsevier Science

Cover of the book Encyclopedia of Stress by R. Mennicken, M. Möller
Cover of the book Peripheral Neuropathies by R. Mennicken, M. Möller
Cover of the book Fundamentals of Ocean Renewable Energy by R. Mennicken, M. Möller
Cover of the book Ultraviolet Laser Technology and Applications by R. Mennicken, M. Möller
Cover of the book Atlas of the Ultrastructure of Diseased Human Muscle by R. Mennicken, M. Möller
Cover of the book Pulp and Paper Industry by R. Mennicken, M. Möller
Cover of the book The Psychology of the Car by R. Mennicken, M. Möller
Cover of the book Statistical Bioinformatics with R by R. Mennicken, M. Möller
Cover of the book Risk Management for Food Allergy by R. Mennicken, M. Möller
Cover of the book Nanomagnetism by R. Mennicken, M. Möller
Cover of the book Biochemistry of Lipids, Lipoproteins and Membranes by R. Mennicken, M. Möller
Cover of the book Advances in Immunology by R. Mennicken, M. Möller
Cover of the book Progress in Heterocyclic Chemistry by R. Mennicken, M. Möller
Cover of the book Silicate Glasses and Melts by R. Mennicken, M. Möller
Cover of the book Phytochemicals in Plant Cell Cultures by R. Mennicken, M. Möller
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy