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Showing 1 to 16 of 16 for “"Self-adjoint operators."”.
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The sixth-order Krall differential expression and self-adjoint operators.
… we review how this theory was applied to find a self-adjoint operator in L2 \mu(-1, 1) generated by the sixth-order Lagrangian symmetric Krall differential equation, as done by S. M. Loveland. We later construct the self-adjoint operator generated by the Krall differential equation in the …
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Analysis of an inequality concerning perturbation of self-adjoint operators
… Davis and McIntosh proved that if A and B are self-adjoint with dist($\sigma(A),\sigma(B)) \geq \delta$ then there is some $c\sb{sa} < 2$ (independent of A and B) such that $c\sb{sa}\vert\vert\vert AQ - QB\vert\vert\vert \geq \delta\vert\vert\vert Q\vert\vert\vert$ for any Q and any unitary …
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Applied left-definite theory : the Jacobi polynomials, their Sobolev orthogonality, and self-adjoint operators.
… of the Jacobi polynomials and construct a self-adjoint operator in a certain Hilbert-Sobolev space having the entire sequence of Jacobi polynomials as eigenfunctions. The key to this construction is the left-definite theory associated with the Jacobi differential equation, and the …
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A study of the computation and convergence behavior of eigenvalue bounds for self-adjoint operators
The convergence rates for the method of Weinstein and a variant method of Aronszajn known as "truncation including the remainder" are derived in terms of the containment gaps between exact and approximating subspaces, using analytical techniques that arise in part in the convergence analysis of …
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Extensions of the Cayley-Hamilton Theorem with Applications to Elliptic Operators and Frames.
… the Cayley-Hamilton Theorem can be extended to self-adjoint trace-class operators and to closed self-adjoint operators with trace-class resolvent over a separable Hilbert space. Applications of these results include calculating operators resolvents and finding the inverse of a frame operator.</p>
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Boundary Value Problems Of Spaces Of Automorphic Forms
… of Bombieri and Garrett to construct natural self-adjoint operators on spaces of automorphic forms whose only possible discrete spectrum is λ s = s(s − 1) for s in a subset of on-line zeros of an L-function, appearing as a compact period of cuspidal-data Eisenstein series on GL 4 . These ideas …
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Stationary solutions of abstract kinetic equations
… a finite interval [0, r]. T and A are abstract self-adjoint operators in a complex Hilbert space. In the case of the half space problem it is assumed that T is a (possibly) unbounded injection and A is a positive compact perturbation of the identity satisfying a regularity condition, while in …
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Topics in spectral and inverse spectral theory
… is concerned with two major classes of operators and provides various spectral and inverse spectral results for them. In the first part of this work a special class of one-dimensional discrete unitary operators is under investigation. The underlying Weyl-Titchmarsh theory and a Borg-type …
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Operational Calculus
… used for analyzing the behavior of linear operators that arise in the study of ordinary and partial differential equations. Given a linear operator T and a class of functions F, one rigorously defines a new operator f(T) for each f in F and establishes properties of the transformation f -> …
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Self-adjoint extensions to the Dirac Coulomb Hamiltonian
… observables, in this case energy, correspond to self-adjoint operators, in this case the Hamiltonian operator HI, acting on the Hilbert space 7H which describes the system in question. It can easily be shown that self-adjoint operators must have real eigenvalues. The reality of the energy …
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Extension of some theorems of complex functional analysis to linear spaces over the quaternions and Cayley numbers
… these division rings and the rings of bounded operators on these spaces is developed. Examples of finite and infinite dimensional spaces over these division rings are given. Questions concerning linear functionals, the Hahn-Banach Theorem and Reflexivity are considered. The Stone-Weierstrass …
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Almost commuting elements of real rank zero C∗-algebras
… following problem. Suppose that X, Y are bounded self-adjoint operators in a Hilbert space H with their commutator [X; Y ] being small. Such operators are called almost commuting. How close is the pair X; Y to a pair of commuting operators X0; Y 0? In terms of one operator A = X + iY , suppose …
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Dynamics of Classical Systems in the Operator Algebra of Quantum Mechanics
… approach, based on raising and lowering operators, especially using the number representation, provides useful tools for modeling collective dynamics of spatially distributed physical systems in a completely general and precise way. Quantum-like models (not necessarily related to the …
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Asymptotic Behaviour and Derivation of Mean Field Models
… of the spectra of families of unbounded self adjoint operators. In Chapter 6 we show how the instability problem for Vlasov-Maxwell can be reduced to this spectral problem. In Chapter 7 we give a proof of well-posedness of a class of solutions to the Vlasov-Poisson system with unbounded …
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The Foundations of Infinite-Dimensional Spectral Computations
… control. This is done for partial differential operators with coefficients of locally bounded total variation and also for discrete infinite matrix operators. We also show how to compute spectral measures of normal operators (when the spectrum is a subset of a regular enough Jordan curve), …
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On Enforcing Maximum Principles and Element-Wise Species Balance for Advective-Diffusive-Reactive Systems
This dissertation aims at developing robust numerical methodologies to solve advective-diffusive-reactive systems that provide accurate and physical solutions for a wide range of input data (e.g., Péclet and Damköhler numbers) and for complicated geometries. It is well-known that physical …