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Academic literature on the topic 'Hilbert space operators'

Author: Grafiati

Published: 6 September 2023

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Journal articles on the topic "Hilbert space operators"

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Agniel, Vidal. "Unitary skew-dilations of Hilbert space operators." Extracta Mathematicae 35, no. 2 (2020): 137–84. http://dx.doi.org/10.17398/2605-5686.35.2.137.

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Kérchy, László. "Pluquasisimilar Hilbert space operators." Acta Scientiarum Mathematicarum 86, no. 34 (2020): 503–20. http://dx.doi.org/10.14232/actasm-020-973-4.

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Krnić, Mario. "Hilbert-type inequalities for Hilbert space operators." Quaestiones Mathematicae 36, no. 2 (June 2013): 209–23. http://dx.doi.org/10.2989/16073606.2013.801148.

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Jarchow, Hans. "Factoring absolutely summing operators through Hilbert-Schmidt operators." Glasgow Mathematical Journal 31, no. 2 (May 1989): 131–35. http://dx.doi.org/10.1017/s0017089500007643.

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Let K be a compact Hausdorff space, and let C(K) be the corresponding Banach space of continuous functions on K. It is well-known that every 1-summing operator S:C(K)→l2 is also nuclear, and therefore factors S = S1S2, with S1:l2→l2 a Hilbert–Schmidt operator and S1:C(K)→l2 a bounded operator. It is easily seen that this latter property is preserved when C(K) is replaced by any quotient, and that a Banach space X enjoys this property if and only if its second dual, X**, does. This led A. Pełczyński [15] to ask if the second dual of a Banach space X must be isomorphic to a quotient of a C(K)-space if X has the property that every 1-summing operator X-→l2 factors through a Hilbert-Schmidt operator. In this paper, we shall first of all reformulate the question in an appropriate manner and then show that counter-examples are available among super-reflexive Tsirelson-like spaces as well as among quasi-reflexive Banach spaces.

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Carmo, Joao R., and S. Waleed Noor. "Universal composition operators." Journal of Operator Theory 87, no. 1 (December 15, 2021): 137–56. http://dx.doi.org/10.7900/jot.2020aug03.2301.

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A Hilbert space operator U is called \textit{universal} (in the sense of Rota) if every Hilbert space operator is similar to a multiple of U restricted to one of its invariant subspaces. It follows that the \textit{invariant subspace problem} for Hilbert spaces is equivalent to the statement that all minimal invariant subspaces for U are one dimensional. In this article we characterize all linear fractional composition operators Cϕf=f∘ϕ that have universal translates on both the classical Hardy spaces H2(C+) and H2(D) of the half-plane and the unit disk, respectively. The new example here is the composition operator on H2(D) with affine symbol ϕa(z)=az+(1−a) for $0

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Rugiri, Peter Githara. "Spectrum of bounded operators in Hilbert spaces." Editon Consortium Journal of Physical and Applied Sciences 3, no. 1 (August 31, 2023): 102–8. http://dx.doi.org/10.51317/ecjpas.v3i1.411.

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This paper sought to study the spectrum operators by emphasising on condition of commuting operators so as to expose classes of operators. Here study of various classes of bounded operators on a Hilbert space H is one of the most important topics in the preparation of the study of the Hilbert spaces. In case a abounded operator A commutes at least with its own adjoint A* it forms important classes of operators on H, eg normal, unitary, self – adjoint etc. The operators under the study are bounded operators operating in a complete space called Hilbert spaces.

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Vaccaro, John A. "Phase operators on Hilbert space." Physical Review A 51, no. 4 (April 1, 1995): 3309–17. http://dx.doi.org/10.1103/physreva.51.3309.

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Leung, Denny H. "Factoring operators through Hilbert space." Israel Journal of Mathematics 71, no. 2 (December 1990): 225–27. http://dx.doi.org/10.1007/bf02811886.

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Boenkost, W., and F. Constantinescu. "Vertex operators in Hilbert space." Journal of Mathematical Physics 34, no. 8 (August 1993): 3607–15. http://dx.doi.org/10.1063/1.530048.

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Khrushchev, Sergei, and Vladimir Peller. "Hankel operators on Hilbert space." Acta Applicandae Mathematicae 5, no. 1 (January 1986): 96–100. http://dx.doi.org/10.1007/bf00049173.

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Dissertations / Theses on the topic "Hilbert space operators"

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邱彩娜 and Choi-nai Charlies Tu. "Generalized spectral norms of Hilbert space operators." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1997. http://hub.hku.hk/bib/B31220010.

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Tu, Choi-nai Charlies. "Generalized spectral norms of Hilbert space operators /." Hong Kong : University of Hong Kong, 1997. http://sunzi.lib.hku.hk/hkuto/record.jsp?B19737452.

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Tian, Feng. "On commutativity of unbounded operators in Hilbert space." Diss., University of Iowa, 2011. https://ir.uiowa.edu/etd/1095.

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We study several unbounded operators with view to extending von Neumann's theory of deficiency indices for single Hermitian operators with dense domain in Hilbert space. If the operators are non-commuting, the problems are difficult, but special cases may be understood with the use representation theory. We will further study the partial derivative operators in the coordinate directions on the L2 space on various covering surfaces of the punctured plane. The operators are defined on the common dense domain of C∞ functions with compact support, and they separately are essentially selfadjoint, but the unique selfadjoint extensions will be non-commuting. This problem is of a geometric flavor, and we study an index formulation for its solution. The applications include the study of vector fields, the theory of Dirichlet problems for second order partial differential operators (PDOs), Sturm-Liouville problems, H.Weyl's limit-point/limit-circle theory, Schrödinger equations, and more.

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Kiteu, Marco M. "Orbits of operators on Hilbert space and some classes of Banach spaces." Kent State University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=kent1341850621.

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Hansen, A. C. "On the approximation of spectra of linear Hilbert space operators." Thesis, University of Cambridge, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.603665.

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The main topic of this thesis is how to approximate and compute spectra of linear operators on separable Hilbert spaces. We consider several approaches including the finite section method, an infinite-dimensional version of the QR algorithm, as well as pseudospectral techniques. Several new theorems about convergence of the finite section method (and variants of it) for self-adjoint problems are obtained together with a rigorous analysis of the infinite-dimensional QR algorithm for normal operators. To attack the general spectral problem we look to the pseudospectral theory and introduce the complexity index. A generalization of the pseudospectrum is introduced, namely, the n-pseudospectrum. This set behaves very much like the original pseudospectrum, but has the advantage that it approximates the spectrum well for large n. The complexity index is a tool for indicating how complex or difficult it may be to approximate spectra of operators belonging to a certain class. We establish bounds on the complexity indeed and discuss some open problems regarding this new mathematical entity. As the approximation framework also gives rise to several computational methods, we analyze and discuss implementation techniques for algorithms that can be derived from the theoretical model. In particular, we develop algorithms that can compute spectra of arbitrary bounded operators on separable Hilbert spaces, and the exposition is followed by several numerical examples. The thesis also contains a thorough discussion on how to implement the QR algorithm in infinite dimensions. This is supported by numerical computations. These examples reveal several surprisingly nice features of the infinite-dimensional QR algorithm, and this leaves a number of open problems that we debate.

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Guven, Ayse. "Quantitative perturbation theory for compact operators on a Hilbert space." Thesis, Queen Mary, University of London, 2016. http://qmro.qmul.ac.uk/xmlui/handle/123456789/23197.

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This thesis makes novel contributions to a problem of practical and theoretical importance, namely how to determine explicitly computable upper bounds for the Hausdorff distance of the spectra of two compact operators on a Hilbert space in terms of the distance of the two operators in operator norm. It turns out that the answer depends crucially on the speed of decay of the sequence of singular values of the two operators. To this end, 'compactness classes', that is, collections of operators the singular values of which decay at a certain speed, are introduced and their functional analytic properties studied in some detail. The main result of the thesis is an explicit formula for the Hausdorff distance of the spectra of two operators belonging to the same compactness class. Along the way, upper bounds for the resolvents of operators belonging to a particular compactness class are established, as well as novel bounds for determinants of trace class operators.

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Alcántara, Bode Julio. "A criteria of completeness for compact operators in Hilbert space." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/97122.

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A necessary and sufficient condition is given for completeness of the set of eigenfunctions and generalized eigenfunctions associated to the non zero eigenvalues of a compact operator on a Hilbert Space.

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Sutton, Daniel Joseph. "Structure of Invariant Subspaces for Left-Invertible Operators on Hilbert Space." Diss., Virginia Tech, 2010. http://hdl.handle.net/10919/28807.

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This dissertation is primarily concerned with studying the invariant subspaces of left-invertible, weighted shifts, with generalizations to left-invertible operators where applicable. The two main problems that are researched can be stated together as When does a weighted shift have the one-dimensional wandering subspace property for all of its closed, invariant subspaces? This can fail either by having a subspace that is not generated by its wandering subspace, or by having a subspace with an index greater than one. For the former we show that every left-invertible, weighted shift is similar to another weighted shift with a residual space, with respect to being generated by the wandering subspace, of dimension $n$, where $n$ is any finite number. For the latter we derive necessary and sufficient conditions for a pure, left-invertible operator with an index of one to have a closed, invariant subspace with an index greater than one. We use these conditions to show that if a closed, invariant subspace for an operator in a class of weighted shifts has a vector in $l^1$, then it must have an index equal to one, and to produce closed, invariant subspaces with an index of two for operators in another class of weighted shifts.
Ph. D.

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Raney, Michael W. "Abstract backward shifts of finite multiplicity /." view abstract or download file of text, 2002. http://wwwlib.umi.com/cr/uoregon/fullcit?p3061962.

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Thesis (Ph. D.)--University of Oregon, 2002.
Typescript. Includes vita and abstract. Includes bibliographical references (leaf 55). Also available for download via the World Wide Web; free to University of Oregon users.

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Kazemi, Parimah. "Compact Operators and the Schrödinger Equation." Thesis, University of North Texas, 2006. https://digital.library.unt.edu/ark:/67531/metadc5453/.

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In this thesis I look at the theory of compact operators in a general Hilbert space, as well as the inverse of the Hamiltonian operator in the specific case of L2[a,b]. I show that this inverse is a compact, positive, and bounded linear operator. Also the eigenfunctions of this operator form a basis for the space of continuous functions as a subspace of L2[a,b]. A numerical method is proposed to solve for these eigenfunctions when the Hamiltonian is considered as an operator on Rn. The paper finishes with a discussion of examples of Schrödinger equations and the solutions.

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Books on the topic "Hilbert space operators"

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Kubrusly, Carlos S. Hilbert Space Operators. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-2064-0.

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Sunder, V. S. Operators on Hilbert Space. Singapore: Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-1816-9.

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Approximation of Hilbert space operators. 2nd ed. Harlow, Essex, England: Longman Scientific & Technical, 1989.

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Hiai, Fumio, and Hideki Kosaki. Means of Hilbert Space Operators. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/b13213.

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Hiai, Fumio. Means of Hilbert space operators. Fukuoka, Japan: Graduate School of Mathematics, Kyushu University, 2002.

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Dunford, Nelson. Linear operators.: Self adjoint operators in Hilbert space. New York: Interscience Publishers, 1988.

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Livšic, Moshe S., and Leonid L. Waksman. Commuting Nonselfadjoint Operators in Hilbert Space. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0078925.

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Axler, Sheldon, Peter Rosenthal, and Donald Sarason, eds. A Glimpse at Hilbert Space Operators. Basel: Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0347-8.

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Sołtan, Piotr. A Primer on Hilbert Space Operators. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-92061-0.

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Blank, Jiří. Hilbert space operators in quantum physics. 2nd ed. [Dordrecht, Netherlands]: Springer, 2008.

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Book chapters on the topic "Hilbert space operators"

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Kubrusly, Carlos S. "Quasireducible Operators." In Hilbert Space Operators, 117–28. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-2064-0_11.

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Kubrusly, Carlos S. "Hyponormal Operators." In Hilbert Space Operators, 65–74. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-2064-0_7.

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Kubrusly, Carlos S. "Paranormal Operators." In Hilbert Space Operators, 93–108. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-2064-0_9.

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Kubrusly, Carlos S. "Hilbert Space Operators." In Hilbert Space Operators, 13–22. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-2064-0_2.

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Farenick, Douglas. "Hilbert Space Operators." In Fundamentals of Functional Analysis, 329–92. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-45633-1_10.

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Kubrusly, Carlos S. "Invariant Subspaces." In Hilbert Space Operators, 1–11. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-2064-0_1.

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Kubrusly, Carlos S. "Proper Contractions." In Hilbert Space Operators, 109–16. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-2064-0_10.

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Kubrusly, Carlos S. "The Lomonosov Theorem." In Hilbert Space Operators, 129–42. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-2064-0_12.

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Kubrusly, Carlos S. "Convergence and Stability." In Hilbert Space Operators, 23–32. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-2064-0_3.

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Kubrusly, Carlos S. "Reducing Subspaces." In Hilbert Space Operators, 33–40. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-2064-0_4.

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Conference papers on the topic "Hilbert space operators"

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Lange, H. J. "Spectral representation of linear operators in the Hilbert space." In 1998 4th International Conference on Actual Problems of Electronic Instrument Engineering Proceedings. APEIE-98. IEEE, 1998. http://dx.doi.org/10.1109/apeie.1998.768958.

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JI, UN CIG. "Integral Representation of Hilbert–Schmidt Operators on Boson Fock Space." In Stochastic Analysis: Classical and Quantum - Perspectives of White Noise Theory. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701541_0004.

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Gahinet, P., M. Sorine, A. J. Laub, and C. Kenney. "Stability margins and Lyapunov equations for linear operators in Hilbert space." In 29th IEEE Conference on Decision and Control. IEEE, 1990. http://dx.doi.org/10.1109/cdc.1990.203444.

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BALAZS, Peter. "Banach frames and atomic decompositions in the space of bounded operators on Hilbert spaces." In 2019 13th International conference on Sampling Theory and Applications (SampTA). IEEE, 2019. http://dx.doi.org/10.1109/sampta45681.2019.9030926.

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Unser, Michael A. "General Hilbert space framework for the discretization of continuous signal processing operators." In SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, edited by Andrew F. Laine and Michael A. Unser. SPIE, 1995. http://dx.doi.org/10.1117/12.217597.

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Balas, Mark J., and Susan A. Frost. "Adaptive Tracking Control for Linear Infinite Dimensional Systems." In ASME 2016 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/smasis2016-9098.

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Tracking an ensemble of basic signals is often required of control systems in general. Here we are given a linear continuous-time infinite-dimensional plant on a Hilbert space and a space of tracking signals generated by a finite basis, and we show that there exists a stabilizing direct adaptive control law that will stabilize the plant and cause it to asymptotically track any member of this collection of signals. The plant is described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on the Hilbert space of states. There is no state or parameter estimation used in this adaptive approach. Our results are illustrated by adaptive control of general linear diffusion systems.

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Balas, Mark J. "Augmentation of Fixed Gain Controlled Infinite Dimensional Systems With Direct Adaptive Control." In ASME 2020 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/imece2020-23179.

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Abstract Linear infinite dimensional systems are described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on a general Hilbert space of states and are controlled via a finite number of actuators and sensors. Many distributed applications are included in this formulation, such as large flexible aerospace structures, adaptive optics, diffusion reactions, smart electric power grids, and quantum information systems. In this paper, we focus on infinite dimensional linear systems for which a fixed gain linear infinite or finite dimensional controller is already in place. We augment this controller with a direct adaptive controller that will maintain stability of the full closed loop system even when the fixed gain controller fails to do so. We prove that the transmission zeros of the combined system are the original open loop transmission zeros, and the point spectrum of the controller alone. Therefore, the combined plant plus controller is Almost Strictly Dissipative (ASD) if and only if the original open loop system is minimum phase, and the fixed gain controller alone is exponentially stable. This result is true whether the fixed gain controller is finite or infinite dimensional. In particular this guarantees that a controller for an infinite dimensional plant based on a reduced -order approximation can be stabilized by augmentation with direct adaptive control to mitigate risks. These results are illustrated by application to direct adaptive control of general linear diffusion systems on a Hilbert space that are described by self-adjoint operators with compact resolvent.

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Cipolla, Jeffrey L. "Transient Infinite Elements for Acoustics and Shock." 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/detc1995-0400.

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Abstract Many phenomena in acoustically loaded structural vibrations are better understood in the time domain, particularly transient radiation, shock, and problems involving nonlinearities and bulk structural motion. In addition, the geometric complexity of structures of interest drives the analyst toward domain-discretized solution methods, such as finite elements or finite differences, and large numbers of degrees of freedom. In such methods, efficient numerical enforcement of the Sommerfeld radiation condition in the time domain becomes difficult; although a great many methodologies for doing so have been demonstrated, there seems to exist no consensus on the optimal numerical implementation of this boundary condition in the time domain. Here, we present theoretical development of several new boundary operators for conventional finite element codes. Each proceeds from successful domain-discretised, projected field-type harmonic solutions, in contrast to boundary integral equation operators or those derived from algebraic functions. We exploit the separable prolate-spheroidal coordinate system, which is sufficiently general for a large variety of problems of naval interest, to obtain finite element-like operators (matrices) for the boundary points. Use of this coordinate system results in element matrices that can be analytically inverse transformed from the frequency to the time domain, using appropriate approximations, without altering the Hilbert space in which the approximate solution resides. The inverse transformation introduces some additional theoretical issues involving time delays and Stieltjes-type integrals, which are easily resolved. In addition, use of element-like boundary operators does not alter the banded structure of the system matrices, which is of enormous importance for efficient solution of large problems. Results presented here include theoretical derivation of the new “infinite elements”, the approximations for certain problematic frequency-domain terms, resolution of the inversion issues, and element matrices for the boundary operators which introduce no new continuity requirements on the fluid field variable.

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Pipek, János, Theodore E. Simos, and George Maroulis. "Quantum Mechanical Operators in Multiresolution Hilbert Spaces." In COMPUTATIONAL METHODS IN SCIENCE AND ENGINEERING: Theory and Computation: Old Problems and New Challenges. Lectures Presented at the International Conference on Computational Methods in Science and Engineering 2007 (ICCMSE 2007): VOLUME 1. AIP, 2007. http://dx.doi.org/10.1063/1.2836134.

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Balas, Mark J., and Susan A. Frost. "A Stabilization of Fixed Gain Controlled Infinite Dimensional Systems by Augmentation With Direct Adaptive Control." In ASME 2017 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/smasis2017-3726.

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Linear infinite dimensional systems are described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on a general Hilbert space of states and are controlled via a finite number of actuators and sensors. Many distributed applications are included in this formulation, such as large flexible aerospace structures, adaptive optics, diffusion reactions, smart electric power grids, and quantum information systems. We have developed the following stability result: an infinite dimensional linear system is Almost Strictly Dissipative (ASD) if and only if its high frequency gain CB is symmetric and positive definite and the open loop system is minimum phase, i.e. its transmission zeros are all exponentially stable. In this paper, we focus on infinite dimensional linear systems for which a fixed gain linear infinite or finite dimensional controller is already in place. It is usually true that fixed gain controllers are designed for particular applications but these controllers may not be able to stabilize the plant under all variations in the operating domain. Therefore we propose to augment this fixed gain controller with a relatively simple direct adaptive controller that will maintain stability of the full closed loop system over a much larger domain of operation. This can ensure that a flexible structure controller based on a reduced order model will still maintain closed-loop stability in the presence of unmodeled system dynamics. The augmentation approach is also valuable to reduce risk in loss of control situations. First we show that the transmission zeros of the augmented infinite dimensional system are the open loop plant transmission zeros and the eigenvalues (or poles) of the fixed gain controller. So when the open-loop plant transmission zeros are exponentially stable, the addition of any stable fixed gain controller does not alter the stability of the transmission zeros. Therefore the combined plant plus controller is ASD and the closed loop stability when the direct adaptive controller augments this combined system is retained. Consequently direct adaptive augmentation of controlled linear infinite dimensional systems can produce robust stabilization even when the fixed gain controller is based on approximation of the original system. These results are illustrated by application to a general infinite dimensional model described by nuclear operators with compact resolvent which are representative of distributed parameter models of mechanically flexible structures. with a reduced order model based controller and adaptive augmentation.

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Reports on the topic "Hilbert space operators"

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Korezlioglu, H., and C. Martias. Stochastic Integration for Operator Valued Processes on Hilbert Spaces and on Nuclear Spaces. Revision. Fort Belvoir, VA: Defense Technical Information Center, March 1986. http://dx.doi.org/10.21236/ada168501.

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