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Showing 1 to 20 of 182 for “"hilbert space"”.
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Optimization Problems in Hilbert Space with POSS Complexes.
<p>Beginning with a survey of functional variation methods in classical physics, we derive the Hartree-Fock theory from canonical quantization. Following a development of density functional theory, many-body perturbation theory, and other techniques of computational condensed matter physics, we …
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Frames and reproducing kernels in a Hilbert space
Let H be a Hilbert space. A set of vectors [Special characters omitted.] ∈ H, i = 1, 2,..., n , x ∈ X , where X is a locally compact space with Borel measure v on it, constitute a rank-n continuous frame, F ([Special characters omitted.] , A, n ) if for each x ∈ X the set [Special characters …
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Hilbert Space Projections and the Navier-Stokes Equation
Unfortunately, but not surprisingly, there arises a closure difficulty: the reduced set of physically admissible measures is still large. In this thesis a particular subclass of admissible measures is studied using the physically based theory of high field sensitivity. The projection associated …
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Calibration of Option Pricing in Reproducing Kernel Hilbert Space
… the local volatility in a reproducing kernel Hilbert space. We defined a new volatility function which allows us to embrace both the financial and time factors of the options. We discuss the existence of the minimizer by using regu- larized reproducing kernel method and show that the …
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Some Aspects of Abstract Linear Evolution Equations in Hilbert Space
Made available in DSpace on 2014-12-09T22:17:38Z (GMT). No. of bitstreams: 1 6801727.pdf: 3737944 bytes, checksum: 68a2566d0dddacc968d03c7a1da36ca8 (MD5) Previous issue date: 1967
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Spectral Decomposition of Stochastic Processes With Parameter in a Hilbert Space
Made available in DSpace on 2014-12-11T18:23:37Z (GMT). No. of bitstreams: 1 7114754.pdf: 1117598 bytes, checksum: 6eecadb746524d93c26a95dae682da84 (MD5) Previous issue date: 1970
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Structure of Invariant Subspaces for Left-Invertible Operators on Hilbert Space
… 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 …
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Functional regression models in the frame work of reproducing kernel Hilbert space
… distance between the null and the alternative space that still allows a possible test. The lower bound of the minimax decay rate of this distance is derived, and test with a distance that decays faster than the lower bound would be impossible. It is shown that the minimax optimal rate is …
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A Hilbert Space Geometric Representation of Shared Awareness and Joint Decision Making
… complex situations. The event representation in Hilbert space provides the necessary foundation to represent an individual's knowledge of a situation. Hilbert space allows representing awareness as a superposition of indefinite states. These states form a complete N-dimensional Hilbert space. …
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Qualitative Behavior of Solutions to Differential Equations in <i>R</i><sup><em>n</em></sup> and in Hilbert Space
The qualitative behavior of solutions of differential equations mainly addresses the various questions arising in the study of the long run behavior of solutions. The contents of this thesis are related to three of the major problems of the qualitative theory, namely the stability, the boundedness …
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Design and Simulation of a Model Reference Adaptive Control System Employing Reproducing Kernel Hilbert Space for Enhanced Flight Control of a Quadcopter
… presents the integration of reproducing kernel Hilbert spaces (RKHSs) into the model reference adaptive control (MRAC) framework to enhance the control systems of quadcopters. Traditional MRAC systems, while robust under predictable conditions, can struggle with the dynamic uncertainties typical …
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Ideals in von Neumann algebras and in associated operator algebras
The compact operators on a Hilbert space are those operators for which the image of the unit ball is relatively compact in the norm topology. These operators form an ideal, in the algebra of all continuous linear operators on the Hilbert space, which is closed in the uniform norm. In the case that …
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Signal detection in fractional Gaussian noise and an RKHS approach to robust detection and estimation
… results related to the reproducing kernel Hilbert space of fractional Brownian motion are presented. In particular, this reproducing kernel Hilbert space is characterized completely and an alternative characterization for the restriction of this class of functions to a compact interval …
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Spectral interpretation of zeros of zeta functions
… field we construct an operator on a separable Hilbert space, whose eigenvalues are exactly the critical zeros of the Dedekind zeta function of the number field.</p>
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Partial ordering of weak mutually unbiased bases in finite quantum systems
… {D(d)} of divisors of d. (ii) the set {hd} of subspaces of a finite Hilbert space Hd and subsets of the set {D(d)} of divisors of d. (iii) the set {Y(d)} of subsystems of a finite quantum system ^(d) and subsets of the set {D(d)} of divisors of d. We conclude this work by showing a duality between …
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Boundary value and Wiener-Hopf problems for abstract kinetic equations with nonregular collision operators
… kinetic equation T𝜑(x)′=-A𝜑(x) in the half space {x≥0} with partial range boundary conditions. The function <i>ψ</i> takes values in a Hilbert space H, T is a self adjoint injective operator on H and A is an accretive operator. The first step in the analysis of this boundary value problem is …
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On the Necessity of Complex Numbers in Quantum Mechanics
… representation in real, complex or quaternionic Hilbert spaces as established by Solèr’s theorem (1995) closing a long standing problem that can be traced back to von Neumann’s mathematical formulation of quantum mechanics. However up to now there are no examples of quantum systems described in …
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