Eigenvalues And Completeness For Regular And Simply Irregular Two Point Differential Operators

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Eigenvalues and Completeness for Regular and Simply Irregular Two-Point Differential Operators

John Locker
Eigenvalues and Completeness for Regular and Simply Irregular Two Point Differential Operators Book PDF

Author : John Locker
Publisher : American Mathematical Soc.
Page : 194 pages
File Size : 44,8 Mb
Release : 2008
Category : Differential operators
ISBN : 9780821841716

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Eigenvalues and Completeness for Regular and Simply Irregular Two-Point Differential Operators by John Locker Pdf

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.

Eigenvalues and Completeness for Regular and Simply Irregular Two-Point Differential Operators

John Locker
Eigenvalues and Completeness for Regular and Simply Irregular Two Point Differential Operators Book PDF

Author : John Locker
Publisher : American Mathematical Society(RI)
Page : 194 pages
File Size : 45,5 Mb
Release : 2014-09-11
Category : Differential operators
ISBN : 1470405172

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Eigenvalues and Completeness for Regular and Simply Irregular Two-Point Differential Operators by John Locker Pdf

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 $B 1, \ldots, B n$.

A Proof of Alon's Second Eigenvalue Conjecture and Related Problems

Joel Friedman
A Proof of Alon s Second Eigenvalue Conjecture and Related Problems Book PDF

Author : Joel Friedman
Publisher : American Mathematical Soc.
Page : 114 pages
File Size : 55,7 Mb
Release : 2008
Category : Eigenvalues
ISBN : 9780821842805

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A Proof of Alon's Second Eigenvalue Conjecture and Related Problems by Joel Friedman Pdf

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.

Regular Subgroups of Primitive Permutation Groups

Martin W. Liebeck,Cheryl E. Praeger,Jan Saxl
Regular Subgroups of Primitive Permutation Groups Book PDF

Author : Martin W. Liebeck,Cheryl E. Praeger,Jan Saxl
Publisher : American Mathematical Soc.
Page : 87 pages
File Size : 48,8 Mb
Release : 2010
Category : Finite simple groups
ISBN : 9780821846544

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Regular Subgroups of Primitive Permutation Groups by Martin W. Liebeck,Cheryl E. Praeger,Jan Saxl Pdf

Addresses the classical problem of determining finite primitive permutation groups G with a regular subgroup B.

Points and Curves in the Monster Tower

Richard Montgomery,Mikhail Zhitomirski_
Points and Curves in the Monster Tower Book PDF

Author : Richard Montgomery,Mikhail Zhitomirski_
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 50,9 Mb
Release : 2010-01-15
Category : Mathematics
ISBN : 9780821848180

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Points and Curves in the Monster Tower by Richard Montgomery,Mikhail Zhitomirski_ Pdf

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.

Unitary Invariants in Multivariable Operator Theory

Gelu Popescu
Unitary Invariants in Multivariable Operator Theory Book PDF

Author : Gelu Popescu
Publisher : American Mathematical Soc.
Page : 105 pages
File Size : 51,6 Mb
Release : 2009-06-05
Category : Mathematics
ISBN : 9780821843963

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Unitary Invariants in Multivariable Operator Theory by Gelu Popescu Pdf

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 $F_n^\infty$.

Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules

AndrŽ Martinez,Vania Sordoni
Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules Book PDF

Author : AndrŽ Martinez,Vania Sordoni
Publisher : American Mathematical Soc.
Page : 96 pages
File Size : 41,5 Mb
Release : 2009-06-05
Category : Mathematics
ISBN : 9780821842966

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Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules by AndrŽ Martinez,Vania Sordoni Pdf

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.

Mixed-Norm Inequalities and Operator Space $L_p$ Embedding Theory

Marius Junge,Javier Parcet
Mixed Norm Inequalities and Operator Space L p Embedding Theory Book PDF

Author : Marius Junge,Javier Parcet
Publisher : American Mathematical Soc.
Page : 168 pages
File Size : 47,9 Mb
Release : 2010
Category : Banach spaces
ISBN : 9780821846551

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Mixed-Norm Inequalities and Operator Space $L_p$ Embedding Theory by Marius Junge,Javier Parcet Pdf

Contains the proof of a noncommutative analogue of the inequality for sums of free random variables over a given von Neumann subalgebra.

Center Manifolds for Semilinear Equations with Non-Dense Domain and Applications to Hopf Bifurcation in Age Structured Models

Pierre Magal,Shigui Ruan
Center Manifolds for Semilinear Equations with Non Dense Domain and Applications to Hopf Bifurcation in Age Structured Models Book PDF

Author : Pierre Magal,Shigui Ruan
Publisher : American Mathematical Soc.
Page : 84 pages
File Size : 45,5 Mb
Release : 2009
Category : Bifurcation theory
ISBN : 9780821846537

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Center Manifolds for Semilinear Equations with Non-Dense Domain and Applications to Hopf Bifurcation in Age Structured Models by Pierre Magal,Shigui Ruan Pdf

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.

Cohomological Invariants: Exceptional Groups and Spin Groups

Skip Garibaldi
Cohomological Invariants Exceptional Groups and Spin Groups Book PDF

Author : Skip Garibaldi
Publisher : American Mathematical Soc.
Page : 102 pages
File Size : 52,9 Mb
Release : 2009-06-05
Category : Mathematics
ISBN : 9780821844045

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Cohomological Invariants: Exceptional Groups and Spin Groups by Skip Garibaldi Pdf

This volume concerns invariants of $G$-torsors with values in mod $p$ Galois cohomology--in the sense of Serre's lectures in the book Cohomological invariants in Galois cohomology--for various simple algebraic groups $G$ and primes $p$. The author determines the invariants for the exceptional groups $F_4$ mod 3, simply connected $E_6$ mod 3, $E_7$ mod 3, and $E_8$ mod 5. He also determines the invariants of $\mathrm{Spin}_n$ mod 2 for $n \leq 12$ and constructs some invariants of $\mathrm{Spin}_{14}$. Along the way, the author proves that certain maps in nonabelian cohomology are surjective. These surjectivities give as corollaries Pfister's results on 10- and 12-dimensional quadratic forms and Rost's theorem on 14-dimensional quadratic forms. This material on quadratic forms and invariants of $\mathrm{Spin}_n$ is based on unpublished work of Markus Rost. An appendix by Detlev Hoffmann proves a generalization of the Common Slot Theorem for 2-Pfister quadratic forms.

The Minimal Polynomials of Unipotent Elements in Irreducible Representations of the Classical Groups in Odd Characteristic

Irina D. Suprunenko
The Minimal Polynomials of Unipotent Elements in Irreducible Representations of the Classical Groups in Odd Characteristic Book PDF

Author : Irina D. Suprunenko
Publisher : American Mathematical Soc.
Page : 168 pages
File Size : 41,6 Mb
Release : 2009-06-05
Category : Mathematics
ISBN : 9780821843697

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The Minimal Polynomials of Unipotent Elements in Irreducible Representations of the Classical Groups in Odd Characteristic by Irina D. Suprunenko Pdf

The minimal polynomials of the images of unipotent elements in irreducible rational representations of the classical algebraic groups over fields of odd characteristic are found. These polynomials have the form $(t-1)^d$ and hence are completely determined by their degrees. In positive characteristic the degree of such polynomial cannot exceed the order of a relevant element. It occurs that for each unipotent element the degree of its minimal polynomial in an irreducible representation is equal to the order of this element provided the highest weight of the representation is large enough with respect to the ground field characteristic. On the other hand, classes of unipotent elements for which in every nontrivial representation the degree of the minimal polynomial is equal to the order of the element are indicated. In the general case the problem of computing the minimal polynomial of the image of a given element of order $p^s$ in a fixed irreducible representation of a classical group over a field of characteristic $p>2$ can be reduced to a similar problem for certain $s$ unipotent elements and a certain irreducible representation of some semisimple group over the field of complex numbers. For the latter problem an explicit algorithm is given. Results of explicit computations for groups of small ranks are contained in Tables I-XII. The article may be regarded as a contribution to the programme of extending the fundamental results of Hall and Higman (1956) on the minimal polynomials from $p$-solvable linear groups to semisimple groups.

Uniqueness and Stability in Determining a Rigid Inclusion in an Elastic Body

Antonino Morassi,Edi Rosset
Uniqueness and Stability in Determining a Rigid Inclusion in an Elastic Body Book PDF

Author : Antonino Morassi,Edi Rosset
Publisher : American Mathematical Soc.
Page : 74 pages
File Size : 55,7 Mb
Release : 2009-06-05
Category : Mathematics
ISBN : 9780821843253

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Uniqueness and Stability in Determining a Rigid Inclusion in an Elastic Body by Antonino Morassi,Edi Rosset Pdf

The authors consider the inverse problem of determining a rigid inclusion inside an isotropic elastic body $\Omega$, from a single measurement of traction and displacement taken on the boundary of $\Omega$. For this severely ill-posed problem they prove uniqueness and a conditional stability estimate of log-log type.

Small Divisor Problem in the Theory of Three-Dimensional Water Gravity Waves

GŽrard Iooss,Pavel I. Plotnikov
Small Divisor Problem in the Theory of Three Dimensional Water Gravity Waves Book PDF

Author : GŽrard Iooss,Pavel I. Plotnikov
Publisher : American Mathematical Soc.
Page : 144 pages
File Size : 51,6 Mb
Release : 2009-06-05
Category : Science
ISBN : 9780821843826

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Small Divisor Problem in the Theory of Three-Dimensional Water Gravity Waves by GŽrard Iooss,Pavel I. Plotnikov Pdf

The authors consider doubly-periodic travelling waves at the surface of an infinitely deep perfect fluid, only subjected to gravity $g$ and resulting from the nonlinear interaction of two simply periodic travelling waves making an angle $2\theta$ between them. Denoting by $\mu =gL/c^{2}$ the dimensionless bifurcation parameter ( $L$ is the wave length along the direction of the travelling wave and $c$ is the velocity of the wave), bifurcation occurs for $\mu = \cos \theta$. For non-resonant cases, we first give a large family of formal three-dimensional gravity travelling waves, in the form of an expansion in powers of the amplitudes of two basic travelling waves. ``Diamond waves'' are a particular case of such waves, when they are symmetric with respect to the direction of propagation. The main object of the paper is the proof of existence of such symmetric waves having the above mentioned asymptotic expansion. Due to the occurence of small divisors, the main difficulty is the inversion of the linearized operator at a non trivial point, for applying the Nash Moser theorem. This operator is the sum of a second order differentiation along a certain direction, and an integro-differential operator of first order, both depending periodically of coordinates. It is shown that for almost all angles $\theta$, the 3-dimensional travelling waves bifurcate for a set of ``good'' values of the bifurcation parameter having asymptotically a full measure near the bifurcation curve in the parameter plane $(\theta,\mu ).$

On the convergence of $\sum c_kf(n_kx)$

Istvan Berkes,Michel Weber
On the convergence of sum c kf n kx Book PDF

Author : Istvan Berkes,Michel Weber
Publisher : American Mathematical Soc.
Page : 88 pages
File Size : 48,7 Mb
Release : 2009
Category : Convergence
ISBN : 9780821843246

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On the convergence of $\sum c_kf(n_kx)$ by Istvan Berkes,Michel Weber Pdf

Presents a general study of the convergence problem and intends to prove several fresh results and improve a number of old results in the field. This title studies the case when the nk are random and investigates the discrepancy the sequence (nkx) mod 1.

Noncommutative Curves of Genus Zero

Dirk Kussin
Noncommutative Curves of Genus Zero Book PDF

Author : Dirk Kussin
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 47,6 Mb
Release : 2009-08-07
Category : Mathematics
ISBN : 9780821844007

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Noncommutative Curves of Genus Zero by Dirk Kussin Pdf

In these notes the author investigates noncommutative smooth projective curves of genus zero, also called exceptional curves. As a main result he shows that each such curve $\mathbb{X}$ admits, up to some weighting, a projective coordinate algebra which is a not necessarily commutative graded factorial domain $R$ in the sense of Chatters and Jordan. Moreover, there is a natural bijection between the points of $\mathbb{X}$ and the homogeneous prime ideals of height one in $R$, and these prime ideals are principal in a strong sense.