Готові списки джерел за темами / Essentially self-adjoint

Добірка наукової літератури з теми "Essentially self-adjoint"

Автор: Grafiati

Опубліковано: 10 грудня 2022

Оновлено: 29 січня 2023

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Статті в журналах з теми "Essentially self-adjoint"

Sebestyén, Zoltán, and Zsigmond Tarcsay. "Characterizations of essentially self-adjoint and skew-adjoint operators." Studia Scientiarum Mathematicarum Hungarica 52, no. 3 (September 2015): 371–85. http://dx.doi.org/10.1556/012.2015.52.3.1300.

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An extension of von Neumann’s characterization of essentially selfadjoint operators is given among not necessarily densely defined symmetric operators which are assumed to be closable. Our arguments are of algebraic nature and follow the idea of [1].

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Khrushchev, S. V. "Uniqueness theorems and essentially self-adjoint operators." Journal of Soviet Mathematics 36, no. 3 (February 1987): 403–8. http://dx.doi.org/10.1007/bf01839612.

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Kalf, H., and F. S. Rofe-Beketov. "On the essential self-adjointness of Schrödinger operators with locally integrable potentials." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 128, no. 1 (1998): 95–106. http://dx.doi.org/10.1017/s0308210500027177.

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Results by Simader, Brézis and Cycon of the genre ‘locally essentially self-adjoint implies globally essentially self-adjoint’ are generalised to Schrödinger operators that are not necessarily bounded from below.

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Falomir, H. A., and P. A. G. Pisani. "Spectral functions of non-essentially self-adjoint operators." Journal of Physics A: Mathematical and Theoretical 45, no. 37 (September 4, 2012): 374017. http://dx.doi.org/10.1088/1751-8113/45/37/374017.

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Kappeler, Th. "Positive perturbations of self-adjoint Schrödinger operators." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 99, no. 3-4 (1985): 241–48. http://dx.doi.org/10.1017/s0308210500014268.

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SynopsisIn this paper, we prove that a positive perturbation T = T0 + q (q ≧ 0 and in ) of an essentially self-adjoint Schrödinger operator T0 = −Δ + q0 on is again essentially self-adjoint if T is relatively bounded with respect to T0. An application of the method of the proof to positive approximations of elements u ≧ 0 in D(T) by a positive sequence in is given.

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Fatehi, Mahsa, and Mahmood Haji Shaabani. "Certain nontrivially essentially self-adjoint weighted composition operators onH2and." Complex Variables and Elliptic Equations 59, no. 12 (January 28, 2014): 1626–35. http://dx.doi.org/10.1080/17476933.2013.870560.

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Neidhardt, Hagen, and Valentin Zagrebnov. "On the Right Hamiltonian for Singular Perturbations: General Theory." Reviews in Mathematical Physics 09, no. 05 (July 1997): 609–33. http://dx.doi.org/10.1142/s0129055x97000221.

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Let the pair of self-adjoint operators {A≥0,W≤0} be such that: (a) there is a dense domain [Formula: see text] such that [Formula: see text] is semibounded from below (stability domain), (b) the symmetric operator [Formula: see text] is not essentially self-adjoint (singularity of the perturbation), (c) the Friedrichs extension [Formula: see text] of [Formula: see text] is maximal with respect to W, i.e., [Formula: see text]. [Formula: see text]. Let [Formula: see text] be a regularizing sequence of bounded operators which tends in the strong resolvent sense to W. The abstract problem of the right Hamiltonian is: (i) to give conditions such that the limit H of self-adjoint regularized Hamiltonians [Formula: see text] exists and is unique for any self-adjoint extension [Formula: see text] of [Formula: see text], (ii) to describe the limit H. We show that under the conditions (a)–(c) there is a regularizing sequence [Formula: see text] such that [Formula: see text] tends in the strong resolvent sense to unique (right Hamiltonian) [Formula: see text], otherwise the limit is not unique.

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ICHINOSE, TAKASHI, and WATARU ICHINOSE. "ON THE ESSENTIAL SELF-ADJOINTNESS OF THE RELATIVISTIC HAMILTONIAN WITH A NEGATIVE SCALAR POTENTIAL." Reviews in Mathematical Physics 07, no. 05 (July 1995): 709–21. http://dx.doi.org/10.1142/s0129055x95000281.

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The relativistic quantum Hamiltonian H describing a spinless particle in an electromagnetic field is considered. H is associated with the classical Hamiltonian [Formula: see text] via Weyl’s correspondence. In the previous papers the second author has proved that H is essentially self-adjoint on [Formula: see text] if the scalar potential V(x) is a function bounded from below by a polynomial in x. In the present paper this result will be extended to show that H is essentially self-adjoint there if V(x) is bounded from below by -C exp a|x| for some positive constants C and a. Ameliorated is also the condition on the vector potential A(x). The result of this kind is quite different from that on the non-relativistic operator, i.e. the Schrödinger operator, but much closer to that on the Dirac operator.

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ALBEVERIO, SERGIO, and VOLODYMYR KOSHMANENKO. "ON THE PROBLEM OF THE RIGHT HAMILTONIAN UNDER SINGULAR FORM-SUM PERTURBATIONS." Reviews in Mathematical Physics 12, no. 01 (January 2000): 1–24. http://dx.doi.org/10.1142/s0129055x00000022.

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Let a perturbation of the self-adjoint operator H0>0 in the Hilbert space ℋ be given by an operator V (or by a quadratic form ν) which is possibly singular and in general nonpositive, so H0+V on [Formula: see text] is only a symmetric operator with nontrivial deficiency indices. The definition of the sum [Formula: see text] in the sense of quadratic forms is extended to cases which are not covered by the well-known KLMN-theorem and conditions are found which ensure the unique self-adjoint realization of H in ℋ. It is also shown that ℋ coincides with the strong resolvent limit of the approximating sequence Hn = H0+Vn, where Vn are bounded self-adjoint operators such that Vn → V in a suitable sense. Essentially that operator V might be strongly singular and acts in the H0-scale of spaces, V:ℋ+→ℋ-.

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MILATOVIC, OGNJEN. "POSITIVE PERTURBATIONS OF SELF-ADJOINT SCHRÖDINGER OPERATORS ON RIEMANNIAN MANIFOLDS." International Journal of Geometric Methods in Modern Physics 02, no. 04 (August 2005): 543–52. http://dx.doi.org/10.1142/s0219887805000715.

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We consider a Schrödinger differential expression L0 = ΔM + V0 on a Riemannian manifold (M,g) with metric g, where ΔM is the scalar Laplacian on M and V0 is a real-valued locally square integrable function on M. We consider a perturbation L0 + V, where V is a non-negative locally square-integrable function on M, and give sufficient conditions for L0 + V to be essentially self-adjoint on [Formula: see text]. This is an extension of a result of T. Kappeler.

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Дисертації з теми "Essentially self-adjoint"

Castillon, Philippe. "Sur les sous-variétés à courbure moyenne constante dans l'espace hyperbolique." Université Joseph Fourier (Grenoble), 1997. http://www.theses.fr/1997GRE10006.

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Dans les chapitres 2 et 3 de cette these, on s'interesse aux sous-varietes de l'espace hyperbolique dont la courbure moyenne est constante et strictement inferieure a un. Le premier resultat qu'on obtient concerne l'operateur de stabilite. Dans notre cas, cet operateur est essentiellement auto-adjoint, et on connait un minorant positif de son spectre essentiel. On montre que le nombre de valeurs propres inferieures a ce minorant est fini, et on en obtient un majorant qui fait intervenir la courbure totale. Ce faisant, on obtient un majorant de l'indice de morse de sous-variete. Un des points importants de la preuve est de controler le noyau de la chaleur de la sous-variete. On obtient ce controle en montrant qu'on a sur la sous-variete des inegalites isoperimetriques. Le second resultat porte sur la compactification. On etend aux sous-varietes a courbure moyenne constantes un resultat de g. De oliveira pour les sous-varietes minimales: on montre que la sous-variete est diffeomorphe a l'interieur d'une variete compact a bord, et que l'immersion s'etend continument au bord en une application a valeurs dans le compactifie de l'espace hyperbolique. Dans le chapitre 4, on etudie les surfaces de revolution a courbure moyenne constante dans l'espace hyperbolique. On obtient une construction cinematique de leurs meridiennes analogue a celle donne par c. Delaunay dans l'espace euclidien. Les courbes a faire rouler ont des proprietes focales similaires a celles des coniques euclidiennes. On trouve les analogues hyperboliques des ellipses, des hyperboles ainsi qu'une surprenante famille de paraboles

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Bandara, Lashi. "Geometry and the Kato square root problem." Phd thesis, 2013. http://hdl.handle.net/1885/10690.

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The primary focus of this thesis is to consider Kato square root problems for various divergence-form operators on manifolds. This is the study of perturbations of second-order differential operators by bounded, complex, measurable coefficients. In general, such operators are not self-adjoint but uniformly elliptic. The Kato square root problem is then to understand when the square root of such an operator, which exists due to uniform ellipticity, is comparable to its unperturbed counterpart. A remarkably adaptable operator-theoretic framework due to Axelsson, Keith and McIntosh sits in the background of this work. This framework allows us to take a powerful first-order perspective of the problems which we consider in a geometric setting. Through a well established procedure, we reduce these problems to the study of quadratic estimates. Under a set of natural conditions, we prove quadratic estimates for a class of operators on vector bundles over complete measure metric spaces. The first kind of estimates we prove are global, and we establish them on trivial vector bundles when the underlying measure grows at most polynomially. The second kind are local, and there, we allow the vector bundle to be non-trivial but bounded in an appropriate sense. Here, the measure is allowed to grow exponentially. An important consequence of obtaining quadratic estimates on measure metric spaces is that it allows us to consider subelliptic operators on Lie groups. The first-order perspective allows us to reduce the subelliptic problem to a fully elliptic one on a sub-bundle. As a consequence, we are able to solve a homogeneous Kato square root problem for perturbations of subelliptic operators on nilpotent Lie groups. For general Lie groups we solve a similar inhomogeneous problem. In the situation of complete Riemannian manifolds, we consider uniformly elliptic divergence-form operators arising from connections on vector bundles. Under a set of assumptions, we show that the Kato square root problem can be solved for such operators. As a consequence, we solve this problem on functions under the condition that the Ricci curvature and injectivity radius are bounded. Assuming an additional lower bound for the curvature endomorphism on forms, we solve a similar problem for perturbations of inhomogeneous Hodge-Dirac operators. A theorem for tensors is obtained by additionally assuming boundedness of a second-order Riesz transform. Motivated by the study of these Kato problems, where for technical reasons it is useful to know the density of compactly supported functions in the domains of operators, we study connections and their divergence on a vector bundle. Through a first-order formulation, we show that this density property holds for the domains of these operators if the metric and connection are compatible and the underlying manifold is complete. We also show that compactly supported functions are dense in the second-order Sobolev space on complete manifolds under the sole assumption that the Ricci curvature is bounded below, improving a result that previously required an additional lower bound on the injectivity radius.

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Книги з теми "Essentially self-adjoint"

Edmunds, D. E., and W. D. Evans. Essential Spectra. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.003.0009.

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In this chapter, various essential spectra are studied. For a closed operator in a Banach space, a number of different sets have been used for the essential spectrum, the sets being identical for a self-adjoint operator in a Hilbert space. As well as the essential spectra, the changes that occur when the operator is perturbed are discussed. Constant-coefficient differential operators are studied in detail.

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Edmunds, D. E., and W. D. Evans. Second-Order Differential Operators on Arbitrary Open Sets. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.003.0007.

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In this chapter, three different methods are described for obtaining nice operators generated in some L2 space by second-order differential expressions and either Dirichlet or Neumann boundary conditions. The first is based on sesquilinear forms and the determination of m-sectorial operators by Kato’s First Representation Theorem; the second produces an m-accretive realization by a technique due to Kato using his distributional inequality; the third has its roots in the work of Levinson and Titchmarsh and gives operators T that are such that iT is m-accretive. The class of such operators includes the self-adjoint operators, even ones that are not bounded below. The essential self-adjointness of Schrödinger operators whose potentials have strong local singularities are considered, and the quantum-mechanical interpretation of essential self-adjointness is discussed.

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Частини книг з теми "Essentially self-adjoint"

"Essential Spectrum of Self-Adjoint Operators." In Spectral and Scattering Theory for Second-Order Partial Differential Operators, 15–20. Chapman and Hall/CRC, 2017. http://dx.doi.org/10.1201/9781315152905-2.

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Тези доповідей конференцій з теми "Essentially self-adjoint"

Venkatesan, S., and R. Ganesan. "Variability in Dynamic Response of Non Self-Adjoint Mechanical Systems." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0350.

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Abstract Variations in strength, geometric and deterioration characteristics of both materials and machine components are quite common in real-life mechanical systems due to manufacturing defects and measurement errors. Such inherent fluctuations which are unavoidable even with the best quality control measures, are essentially random in nature. Effects of these random fluctuations on the performance levels, dynamic response and service life of mechanical systems need to be evaluated based on a stochastic approach, in order to assist design and diagnostics of industrial machinery. Non self-adjoint eigenproblems that correspond to the dynamic response of complex mechanical systems such as high speed rotors, fluid-flowing pipes and actively controlled structures are considered in the present work. The coefficients of the matrices are stochastic processes and are resulting from uncertain parameters of the mechanical system being described by the eigenproblem. A perturbational solution is sought and obtained in a form that does not involve repeated solutions of a recursive set of equations. Sample functions are generated based on the perturbational expansion and response moments are obtained by treating uncertain fluctuations to be stochastic perturbations. Complete covariance structures of both eigenvalues and eigenvectors are obtained through computationally efficient expressions. Applications of the developed procedure for real-life mechanical systems, that have uncertain material properties, are demonstrated.

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Chung, Chunhui, and Imin Kao. "Study on the Vibration Response of Axially Moving Continua." In ASME 2013 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/dscc2013-3811.

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Axially moving continua such as belt, chain, and conveyer are common transmission components. The study of the vibration response of axially moving continua is an essential topic to understand the fundamentals of vibration and improve the performance of the machines. However, it typically requires more rigorous effort in mathematical derivation to obtain the analytical forced vibration responses of the axially moving continua because of the characteristics of non-self-adjoint equation of motion. The methods utilized to obtain the analytical solutions include the modal analysis, canonical form, wave propagation, Laplace transform, and transfer function. In this review paper, these methods will be reviewed and presented. The advantages and disadvantages of different methodologies are discussed as well.

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