Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 45 for “"Operator theory."”.
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The Pettis Integral and Operator Theory
… if for each x* X*, x*f L1(µ). Define the operator Tf. X* → L1(µ) by T(x*) = x*f. Then f is Pettis integrable if and only if this operator is weak*-to-weak continuous. This paper begins with an overview of this function. Work by Robert Huff and Gunnar Stefansson on the operator Tf motivates …
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Application of Koopman Operator Theory to Legged Locomotion
… a linearized simple walking model using Koopman Operator Theory, and its usage in Linear Model Predictive Control (L-MPC). Various walking and contact models were evaluated, but ultimately the rimless wheel was selected due to its inherent stability and low dimensionality, and a nonlinear …
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Koopman Operator Theory Applied to Lambert’s Problem with a Spectral Behavior Analysis
… have constraints in their applications. Using operator theory to simplify a system’s nonlinear dynamics presents a promising avenue for research. This Thesis bridges the gap in implementing operator theory to effectively solve Lambert’s problem. The Koopman Operator is used to embed the …
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Weak Radon-Nikdoym Sets in Dual Banach Spaces
The interplay between geometry, topology, measure theory and operator theory has long been evident in the study of the Radon-Nikodym property. Recently results of substantial interest in the structure of Banach spaces have been obtained by localizing these ideas to individual subsets. The study of …
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Algebras of Toeplitz Operators
In this work we examine C*-algebras of Toeplitz operators over the unit ball in ℂ<sup>n</sup> and the unit polydisc in ℂ². Toeplitz operators are interesting examples of non-normal operators that generate non-commutative C*-algebras. Moreover, in the nice cases (depending on the geometry of the …
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Some classes of linear and nonlinear operators
… analysis, particularly in the field of Operator theory. The study begins with definitions of linear spaces and some topological results which form the necessary background.Chapter two is the heart of the work and deals with operators defined on a Hilbert space with mention of operators …
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Some classes of linear and nonlinear operators
… analysis, particularly in the field of Operator theory. The study begins with definitions of linear spaces and some topological results which form the necessary background.Chapter two is the heart of the work and deals with operators defined on a Hilbert space with mention of operators …
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Noncommutative Kernels
… of complex analysis and Hilbert-space operator theory, and they have recently been extended to the setting of free noncommutative function theory. In this paper, we develop the subject further in a number of directions. We give a characterization of completely positive noncommutative …
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Unbounded linear operators in seminormed spaces
Linear operator theory is usually studied in the setting of normed or Banach spaces. However, careful examination of proofs shows that in many cases the Hausdorff property of normed spaces is not used. Even in those cases where explicit use of the Hausdorff property is made, one can often get …
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Moment sequences and their applications
… the study of the subnormal completion problem in operator theory. Last, we show that certain power functions are the building blocks of completely positive functions; by our definition, these functions are the continuous functions on the interval [0, 1] that map each Hausdorff moment sequence of a …
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Propagation Failure in Discrete Inhomogeneous Medium Using a Caricature of the Cubic
… reaction term. Using a combination of Jacobi-Operator theory and the Sherman-Morrison formula we de- rive exact solutions in the cases of homogeneous and inhomogeneous diffusion. Solutions exist only under certain conditions outlined in their construction. The range of parameter values that …
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Applications and limits of convex optimization
… Paulsen problem, a longstanding open problem in operator theory, was recently resolved by Kwok et al [40]. We use a convex program due to Barthe to present a dramatically simpler proof with an accompanying efficient algorithm that also achieves a better bound. Next, we examine the related …
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Wavelet-based Dynamic Mode Decomposition in the Context of Extended Dynamic Mode Decomposition and Koopman Theory
Koopman theory is widely used for data-driven modeling of nonlinear dynamical systems. One of the well-known algorithms that stem from this approach is the Extended Dynamic Mode Decomposition (EDMD), a data-driven algorithm for uncontrolled systems. In this thesis, we will start by discussing the …
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On approximation properties of group C* - algebras
In this thesis we study analytic techniques from operator theory that encapsulate geometric properties of a group. Rapid Decay Property (Property RD) provides estimates for the operator norm of elements of the group ring (in the left-regular representation) in terms of the Sobolev norm. Roughly, …
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Rigidity operators and the flexibility of infinite bar-joint frameworks
… various techniques from functional analysis and operator theory to develop the linear infinitesimal theory of crystal frameworks in the Euclidean space Rd. In this mathematical theory we obtain sufficient conditions for the boundedness of the rigidity matrix R(G), viewed as a Hilbert space …
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Closability of differential operators and subjordan operators
A (bounded linear) operator J on a Hilbert space is said to be jordan if J = S + N where S = S* and N² = 0. The operator T is subjordan if T is the restriction of a jordan operator to an invariant subspace, and pure subjordan if no nonzero restriction of T to an invariant subspace is jordan. The …
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Frames In Hilbert C*-modules
… image processing, data compression and sampling theory etc. Today, powerful tools from operator theory and Banach space theory are being introduced to the study of frames producing deep results in frame theory. In recent years, many mathematicians generalized the frame theory from Hilbert spaces …
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Power System Stability Improvement with Decommissioned Synchronous Machine Using Koopman Operator Based Model Predictive Control
… the nonlinear controller design using Koopman operator-based framework is proposed. Besides, the time delay embedding technique is adopted together with Koopman operator theory for the nonlinear system identification. Koopman operator provides a linear representation of the system and thereby …
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Commutators and dyadic paraproducts on weighted Lebesgue spaces
We prove that the operator norm on weighted Lebesgue space L^2(w) of the commutators of the Hilbert, Riesz and Beurling transforms with a BMO function b depends quadratically on the A2 characteristic of the weight, as opposed to the linear dependence known to hold for the operators themselves. It …
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