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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Self-adjoint matrix equations on time scales

Buchholz, Bobbi January 1900 (has links)
Thesis (Ph.D.)--University of Nebraska-Lincoln, 2007. / Title from title screen (site viewed July 9, 2007). PDF text: 96 p. UMI publication number: AAT 3252832. Includes bibliographical references. Also available in microfilm and microfiche formats.
2

Eigenvalue gaps for self-adjoint operators

Michel, Patricia L. 08 1900 (has links)
No description available.
3

Some problems in differential operators (essential self-adjointness)

Keller, R. Godfrey January 1977 (has links)
We consider a formally self-adjoint elliptic differential operator in IR<sup>n</sup>, denoted by τ. T<sub>0</sub> and T are operators given by τ with specific domains. We determine conditions under which T<sub>0</sub> is essentially self-adjoint, introducing the topic by means of a brief historical survey of some results in this field. In Part I, we consider an operator of order 4, and in Part II, we generalise the results obtained there to ones for an operator of order 2m. Thus, the two parts run parallel. In Chapter 1, we determine the domain of T<sub>0</sub>*, denoted by D(T<sub>0</sub>*), where T<sub>0</sub>* denotes the adjoint of T<sub>0</sub>, and introduce operators <u>T</u><sub>0</sub> and <u>T</u> which are modifications of T<sub>0</sub> and T. In Chapter 2, we use a theorem of Schechter to give conditions under which <u>T</u><sub>0</sub> is essentially self-adjoint. Working with the operator <u>T</u>, in Chapter 3 ve show that we can approximate functions u in D(T<sub>0</sub>*) by a particular sequence of test-functions, which enables us to derive an identity involving u, Tu and the coefficient functions of the operator concerned. In Chapter 4, we determine an upper bound for the integral of a function involving a derivative of u in D(T<sub>0</sub>*) whose order is half the order of the operator concerned, and we use the identity from the previous chapter to reformulate this upper bound. In Chapter 5, we give conditions which are sufficient for the essential self-adjointness of T<sub>0</sub>. In the main theorem itself, the major step is the derivation of the integral of the function involving the particular derivative of u in D(T<sub>0</sub>*) whose order is half the order of the operator concerned, referred to above, itself as a term of an upper bound of an integral we wish to estimate. Hence, we can employ the upper bound from Chapter 4. This "sandwiching" technique is basic to the approach we have adopted. We conclude with a brief discussion of the operators we considered, and restate the examples of operators which we showed to be essentially self-adjoint.
4

Applied left-definite theory the Jacobi polynomials, their Sobolev orthogonality, and self-adjoint operators /

Bruder, Andrea S. Littlejohn, Lance L. January 2009 (has links)
Thesis (Ph.D.)--Baylor University, 2009. / Subscript in abstract: n and n=0 in {Pn([alpha],[beta])(x)} [infinity] n=0, [mu] in (f,g)[mu], and R in [integral]Rfgd[mu]. Superscript in abstract: ([alpha],[beta]) and [infinity] in {Pn([alpha],[beta])(x)} [infinity] n=0. Includes bibliographical references (p. 115-119).
5

Extension of positive definite functions

Niedzialomski, Robert 01 May 2013 (has links)
Let $\Omega\subset\mathbb{R}^n$ be an open and connected subset of $\mathbb{R}^n$. We say that a function $F\colon \Omega-\Omega\to\mathbb{C}$, where $\Omega-\Omega=\{x-y\colon x,y\in\Omega\}$, is positive definite if for any $x_1,\ldots,x_m\in\Omega$ and any $c_1,\ldots,c_m\in \mathbb{C}$ we have that $\sum_{j,k=1}^m F(x_j-x_k)c_j\overline{c_k}\geq 0$. Let $F\colon\Omega-\Omega\to\mathbb{C}$ be a continuous positive definite function. We give necessary and sufficient conditions for $F$ to have an extension to a continuous and positive definite function defined on the entire Euclidean space $\mathbb{R}^n$. The conditions are formulated in terms of strong commutativity of some certain selfadjoint operators defined on a Hilbert space associated to our positive definite function.
6

Discrete and continuous inverse boundary problems on a disc /

Ingerman, David V. January 1997 (has links)
Thesis (Ph. D.)--University of Washington, 1997. / Vita. Includes bibliographical references (p. [77]-79).
7

Uma introdução aos operadores de Schrödinger com ênfase no caso unidimensional. / An Introduction to Schrödinger operators with emphasis on one-dimensional case.

Ramos, Priscila Santos 26 February 2009 (has links)
The main objective of this dissertation is to give an introduction to Schrödinger operators of the type H = -&#8710; + V. In these operators, &#8710; denotes the Laplacian of R&#8319; and V denotes the operator of multiplication by a function V both defined in a suitable subspace of L²(R&#8319;) with respect to the determination of its selfadjointess and of its spectrum. / Fundação de Amparo a Pesquisa do Estado de Alagoas / O objetivo principal desta dissertação é fornecer uma introdução aos operadores de Schrödinger do tipo H = -&#8710; + V, onde &#8710; denota o laplaciano do R&#8319; e V denota o operador de multiplicação pela função V ambos definidos em um subespaço conveniente do L²(R&#8319;), no que diz respeito à determinação de sua auto-adjunticidade e do seu espectro.
8

Eigenvalues of compactly perturbed linear operators

Hansmann, Marcel 02 August 2018 (has links)
This cumulative habilitation thesis is concerned with eigenvalues of compactly perturbed operators in Banach and Hilbert spaces. A general theory for studying such eigenvalues is developed and applied to the study of some concrete operators of mathematical physics.
9

Symmetries and conservation laws

Khamitova, Raisa January 2009 (has links)
Conservation laws play an important role in science. The aim of this thesis is to provide an overview and develop new methods for constructing conservation laws using Lie group theory. The derivation of conservation laws for invariant variational problems is based on Noether’s theorem. It is shown that the use of Lie-Bäcklund transformation groups allows one to reduce the number of basic conserved quantities for differential equations obtained by Noether’s theorem and construct a basis of conservation laws. Several examples on constructing a basis for some well-known equations are provided. Moreover, this approach allows one to obtain new conservation laws even for equations without Lagrangians. A formal Lagrangian can be introduced and used for computing nonlocal conservation laws. For self-adjoint or quasi-self-adjoint equations nonlocal conservation laws can be transformed into local conservation laws. One of the fields of applications of this approach is electromagnetic theory, namely, nonlocal conservation laws are obtained for the generalized Maxwell-Dirac equations. The theory is also applied to the nonlinear magma equation and its nonlocal conservation laws are computed.
10

Spektraltheorie gewöhnlicher linearer Differentialoperatoren vierter Ordnung / Spectral Analysis of Fourth Order Differential Operators

Abels, Otto 25 July 2001 (has links)
In this thesis the spectral properties of differential operators generated by the formally self-adjoint differential expression Τy = w⁻₁[(ry″)″ - (py′)′ + qy] are investigated. The main tools to be used are the theory of asymptotic integration and the Titchmarsh--Weyl M-matrix. Subject to certain regularity conditions on the coefficients asymptotic integration leads to estimates for the eigenfunctions of the corresponding differential equation Τy = zy. According to the theory of asymptotic integration the regularity conditions combine smoothness with decay, i.e. admissible coefficients are (in an appropriate sense) either short range or slowly varying. Knowledge of the asymptotics (x → ∞) of the solutions will then be used to determine the deficiency index and to derive properties of the M-matrix which is closely related to the spectral measure of an associated self-adjoint realization Τ. Consequently we can compute the multiplicity of the spectrum, locate the absolutely continuous spectrum and give conditions for the singular continuous spectrum to be empty. This generalizes classical results on second order operators.

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