Eigenvalues And Completeness For Regular And Simply Irregular Two Point Differential Operators
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Author | : John Locker |
Publisher | : American Mathematical Society(RI) |
Total Pages | : 194 |
Release | : 2014-09-11 |
Genre | : Differential operators |
ISBN | : 9781470405175 |
Download Eigenvalues and Completeness for Regular and Simply Irregular Two-Point Differential Operators Book in PDF, Epub and Kindle
In this monograph the author develops the spectral theory for an $n$th order two-point differential operator $L$ in the Hilbert space $L2[0,1]$, where $L$ is determined by an $n$th order formal differential operator $\ell$ having variable coefficients and by $n$ linearly independent boundary values $B 1, \ldots, B n$.
Author | : John Locker |
Publisher | : American Mathematical Soc. |
Total Pages | : 194 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 0821841718 |
Download Eigenvalues and Completeness for Regular and Simply Irregular Two-Point Differential Operators Book in PDF, Epub and Kindle
In this monograph the author develops the spectral theory for an $n$th order two-point differential operator $L$ in the Hilbert space $L2[0,1]$, where $L$ is determined by an $n$th order formal differential operator $\ell$ having variable coefficients and by $n$ linearly independent boundary values $B 1, \ldots, B n$. Using the Birkhoff approximate solutions of the differential equation $(\rhon I - \ell)u = 0$, the differential operator $L$ is classified as belonging to one of threepossible classes: regular, simply irregular, or degenerate irregular. For the regular and simply irregular classes, the author develops asymptotic expansions of solutions of the differential equation $(\rhon I - \ell)u = 0$, constructs the characteristic determinant and Green's function,characterizes the eigenvalues and the corresponding algebraic multiplicities and ascents, and shows that the generalized eigenfunctions of $L$ are complete in $L2[0,1]$. He also gives examples of degenerate irregular differential operators illustrating some of the unusual features of this class.
Author | : Joel Friedman |
Publisher | : American Mathematical Soc. |
Total Pages | : 114 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 0821842803 |
Download A Proof of Alon's Second Eigenvalue Conjecture and Related Problems Book in PDF, Epub and Kindle
A $d$-regular graph has largest or first (adjacency matrix) eigenvalue $\lambda_1=d$. Consider for an even $d\ge 4$, a random $d$-regular graph model formed from $d/2$ uniform, independent permutations on $\{1,\ldots,n\}$. The author shows that for any $\epsilon>0$ all eigenvalues aside from $\lambda_1=d$ are bounded by $2\sqrt{d-1}\;+\epsilon$ with probability $1-O(n^{-\tau})$, where $\tau=\lceil \bigl(\sqrt{d-1}\;+1\bigr)/2 \rceil-1$. He also shows that this probability is at most $1-c/n^{\tau'}$, for a constant $c$ and a $\tau'$ that is either $\tau$ or $\tau+1$ (``more often'' $\tau$ than $\tau+1$). He proves related theorems for other models of random graphs, including models with $d$ odd.
Author | : Tynysbek Sh. Kalmenov |
Publisher | : Springer |
Total Pages | : 485 |
Release | : 2017-12-12 |
Genre | : Mathematics |
ISBN | : 3319670530 |
Download Functional Analysis in Interdisciplinary Applications Book in PDF, Epub and Kindle
This volume presents current research in functional analysis and its applications to a variety of problems in mathematics and mathematical physics. The book contains over forty carefully refereed contributions to the conference “Functional Analysis in Interdisciplinary Applications” (Astana, Kazakhstan, October 2017). Topics covered include the theory of functions and functional spaces; differential equations and boundary value problems; the relationship between differential equations, integral operators and spectral theory; and mathematical methods in physical sciences. Presenting a wide range of topics and results, this book will appeal to anyone working in the subject area, including researchers and students interested to learn more about different aspects and applications of functional analysis.
Author | : Martin W. Liebeck |
Publisher | : American Mathematical Soc. |
Total Pages | : 87 |
Release | : 2010 |
Genre | : Mathematics |
ISBN | : 082184654X |
Download Regular Subgroups of Primitive Permutation Groups Book in PDF, Epub and Kindle
Addresses the classical problem of determining finite primitive permutation groups G with a regular subgroup B.
Author | : Richard Montgomery |
Publisher | : American Mathematical Soc. |
Total Pages | : 154 |
Release | : 2010-01-15 |
Genre | : Mathematics |
ISBN | : 0821848186 |
Download Points and Curves in the Monster Tower Book in PDF, Epub and Kindle
Cartan introduced the method of prolongation which can be applied either to manifolds with distributions (Pfaffian systems) or integral curves to these distributions. Repeated application of prolongation to the plane endowed with its tangent bundle yields the Monster tower, a sequence of manifolds, each a circle bundle over the previous one, each endowed with a rank $2$ distribution. In an earlier paper (2001), the authors proved that the problem of classifying points in the Monster tower up to symmetry is the same as the problem of classifying Goursat distribution flags up to local diffeomorphism. The first level of the Monster tower is a three-dimensional contact manifold and its integral curves are Legendrian curves. The philosophy driving the current work is that all questions regarding the Monster tower (and hence regarding Goursat distribution germs) can be reduced to problems regarding Legendrian curve singularities.
Author | : Gelu Popescu |
Publisher | : American Mathematical Soc. |
Total Pages | : 105 |
Release | : 2009-06-05 |
Genre | : Mathematics |
ISBN | : 0821843966 |
Download Unitary Invariants in Multivariable Operator Theory Book in PDF, Epub and Kindle
This paper concerns unitary invariants for $n$-tuples $T:=(T_1,\ldots, T_n)$ of (not necessarily commuting) bounded linear operators on Hilbert spaces. The author introduces a notion of joint numerical radius and works out its basic properties. Multivariable versions of Berger's dilation theorem, Berger-Kato-Stampfli mapping theorem, and Schwarz's lemma from complex analysis are obtained. The author studies the joint (spatial) numerical range of $T$ in connection with several unitary invariants for $n$-tuples of operators such as: right joint spectrum, joint numerical radius, euclidean operator radius, and joint spectral radius. He also proves an analogue of Toeplitz-Hausdorff theorem on the convexity of the spatial numerical range of an operator on a Hilbert space, for the joint numerical range of operators in the noncommutative analytic Toeplitz algebra $F_n^\infty$.
Author | : Andr Martinez |
Publisher | : American Mathematical Soc. |
Total Pages | : 96 |
Release | : 2009-06-05 |
Genre | : Mathematics |
ISBN | : 082184296X |
Download Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules Book in PDF, Epub and Kindle
The authors construct an abstract pseudodifferential calculus with operator-valued symbol, suitable for the treatment of Coulomb-type interactions, and they apply it to the study of the quantum evolution of molecules in the Born-Oppenheimer approximation, in the case of the electronic Hamiltonian admitting a local gap in its spectrum. In particular, they show that the molecular evolution can be reduced to the one of a system of smooth semiclassical operators, the symbol of which can be computed explicitely. In addition, they study the propagation of certain wave packets up to long time values of Ehrenfest order.
Author | : Marius Junge |
Publisher | : American Mathematical Soc. |
Total Pages | : 168 |
Release | : 2010 |
Genre | : Mathematics |
ISBN | : 0821846558 |
Download Mixed-Norm Inequalities and Operator Space $L_p$ Embedding Theory Book in PDF, Epub and Kindle
Contains the proof of a noncommutative analogue of the inequality for sums of free random variables over a given von Neumann subalgebra.
Author | : Pierre Magal |
Publisher | : American Mathematical Soc. |
Total Pages | : 84 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 0821846531 |
Download Center Manifolds for Semilinear Equations with Non-Dense Domain and Applications to Hopf Bifurcation in Age Structured Models Book in PDF, Epub and Kindle
Several types of differential equations, such as delay differential equations, age-structure models in population dynamics, evolution equations with boundary conditions, can be written as semilinear Cauchy problems with an operator which is not densely defined in its domain. The goal of this paper is to develop a center manifold theory for semilinear Cauchy problems with non-dense domain. Using Liapunov-Perron method and following the techniques of Vanderbauwhede et al. in treating infinite dimensional systems, the authors study the existence and smoothness of center manifolds for semilinear Cauchy problems with non-dense domain. As an application, they use the center manifold theorem to establish a Hopf bifurcation theorem for age structured models.