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This monograph develops the spectral theory of an $n$th order non-self-adjoint two-point differential operator $L$ in the Hilbert space $L^2[0,1]$. The mathematical foundation is laid in the first part, where the spectral theory is developed for closed linear operators and Fredholm operators. An important completeness theorem is established for the Hilbert-Schmidt discrete operators. The operational calculus plays a major role in this general theory. In the second part, the spectral theory of the differential operator $L$ is developed by expressing $L$ in the form $L = T + S$, where $T$ is the principal part determined by the $n$th order derivative and $S$ is the part determined by the lower-order derivatives. The spectral theory of $T$ is developed first using operator theory, and then the spectral theory of $L$ is developed by treating $L$ as a perturbation of $T$. Regular and irregular boundary values are allowed for $T$, and regular boundary values are considered for $L$. Special features of the spectral theory for $L$ and $T$ include the following: calculation of the eigenvalues, algebraic multiplicities and ascents; calculation of the associated family of projections which project onto the generalized eigenspaces; completeness of the generalized eigenfunctions; uniform bounds on the family of all finite sums of the associated projections; and expansions of functions in series of generalized eigenfunctions of $L$ and $T

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- Series:
**Mathematical Surveys and Monographs 073** - Author:
**John Locker** - Year:
**2000** - Publisher:
**American Mathematical Society** - Language:
**English** - ISBN:
**0-8218-2049-4,9780821820490**

- DPI:
**600** - File size:
**2 151 402** - Format:
**djvu**

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The spectral theory of linear operators plays a key role in the mathematical formulation of quantum theory. Furthermore, such a rigorous mathematical foundation leads to a more profound insight into the nature of quantum mechanics. This textbook provides ...

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...

There has recently been a renewal of interest in Fokker-Planck operators, motivated by problems in statistical physics, in kinetic equations and differential geometry. Compared to more standard problems in the spectral theory of partial differential opera...

This volume contains the proceedings of the OTAMP 2008 (Operator Theory, Analysis and Mathematical Physics) conference held at the Mathematical Research and Conference Center in Bedlewo near Poznan. It is composed of original research articles describing ...

The conjugate operator method is a powerful recently developed technique for studying spectral properties of self-adjoint operators. One of the purposes of this volume is to present a refinement of the original method due to Mourre leading to essentially ...

This and the next volume of the OT series contain the proceedings of the WorkÂ shop on Operator Theory and its Applications, IWOTA 95, which was held at the University of Regensburg, Germany, July 31 to August 4, 1995. It was the eigth workshop of this ki...

This textbook provides an introduction to the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators, and spectral theory of self-adjoint operators. It also presents the basic theorems and methods of a...

Since the seminal work of P. Anderson in 1958, localization in disordered systems has been the object of intense investigations. Mathematically speaking, the phenomenon can be described as follows: the self-adjoint operators which are used as Hamiltonians...

It takes a book as versatile as its subject to cover Apache Tomcat, the popular open source Servlet and JSP container and high performance web server. Tomcat: The Definitive Guide is a valuable reference for administrators and webmasters, a useful guide f...

Anna Elisabetta Galeotti examines the most intractable problems which toleration encounters and argues that what is really at stake is not religious or moral disagreement but the unequal status of different social groups. Liberal theories of toleration fa...

" J.R.R. Tolkien's zeal for medieval literary, religious, and cultural ideas deeply influenced his entire life and provided the seeds for his own fiction. In Tolkien's Art, Chance discusses not only such classics as The Hobbit, The Lord of the Rings, and ...

In his 1889 novella The Kreutzer Sonata Lev Tolstoy declared war on human sexuality. Having fathered thirteen children by his wife and at least two children by peasant women, the great Russian writer now has the arrogance to suggest that people should sto...