Spectral Transforms and Operators in Two Dimensions
SCHR ¨ ODINGER OPERATORS IN TWO DIMENSIONS
... with spectral parameters in the lower half plane of the complex plane (unphysical sheet or 2nd sheet) for magnetic Schr¨odinger operators in two ...
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Finite Pseudo-Differential Operators, Localization Operators for Curvelet and Ridgelet Transforms
... Stockwell transforms into a class in its own ...the two-dimensional Stockwell transform and the corresponding resolution of the identity ...Stockwell transforms and their resolution of the identity ...
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SPECTRAL DUALITY FOR UNBOUNDED OPERATORS
... In this paper we take up two themes, one we call spectral reciprocity, and the other is a computational approximation scheme (Sections 5 and 6). Both themes interact with the various related developments ...
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Spectral Theory of PauliFierz Operators
... self-adjoint operators in a Hilbert space decomposed as a direct sum of two Hilbert ...in spectral geometry, number theory and mathematical physics, and we hope that some of the results of this ...
Fourier pseudo spectral method for the extended Fisher Kolmogorov equation in two dimensions
... Fisher-Kolmogorov (EFK) equation plays an important role. In this paper, a Fourier pseudo-spectral method for solving the EFK equation in two space dimensions is presented. Prior bounds are proved ...
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The Spectral Theorem for Self-Adjoint Operators
... The spectral theorem originally arose in the context of operator theory where the proof depended on well known results from measure theory, namely the Riesz Representation Theorem, and direct ...the ...
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Spectral approximation of aperiodic Schrödinger operators
... are two points of view that arise ...the spectral properties do not vary too much? On the other hand, it is common to approximate such an operator whenever the operator H is difficult to ...many ...
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Bootstrapping spectral statistics in high dimensions
... linear spectral statistics (Najim and Yao, 2016), as well as a consistency guarantee for spectrum estimation (Ledoit and Wolf, ...are two ingredients from Najim and Yao (2016) that are helpful in analyzing ...
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Boundedness of Riesz transforms for elliptic operators on abstract Wiener spaces
... semigroup on a Hilbert space H and let −L be the L p -realisation of the generator of its second quantisa- tion. Our results imply that two-sided bounds for the Riesz transform of L are equivalent with the Kato ...
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Two new integral transforms and their applications
... In the first three of the following sections we derive the spectral representation for ( 1.. the gravitational or electrostatic potential outside a sphere. Our transfor[r] ...
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Spectral collocation method for compact integral operators
... Chapter 3 aims to provide algorithms, numerical experiments and convergence analysis for integro-differential equations. In Chapter 4, we will study the algorithms and numerical experiments for eigen- value problems, ...
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Spectral Results for Perturbed Periodic Jacobi Operators
... least two eigenvalues simultaneously with a single ...of spectral parameters, but do not establish how these subordinate solutions can be made into formal ...
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Spectral Edge Properties of Periodic Elliptic Operators
... In particular, we are able to show that the Liouville-Riemann-Roch inequalities hold for ‘generic’ periodic Schrödinger operators at their gap edges and for two-dimensional periodic Schrödinger ...
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Aspects of spectral theory for algebras of measurable operators
... defined operators affiliated to a commutative von Neumann ...-measurable operators, which contains the algebra of τ -measurable operators, and show that it is a ∗-algebra with respect to strong sum, ...
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On Spectral Invariants of Dirac Operators on Noncommutative Tori and Curvature of the Determinant Line Bundle for the Noncommutative Two Torus
... Dirac operators and spectral triples Beyond the noncommuattive topology, the program of noncommutative geometry in the spectral triple picture initiated by Alain Connes [9] is to extend the framework ...
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Efficient Spherical Harmonic Transforms aimed at pseudo-spectral numerical simulations
... to N + 1 being a power of two, requires 2(N + 1) latitudinal colocation points, and crashed for N = 2047. The software library implementing the fast Legendre transform described by Mohlenkamp (1999), libftsh, has ...
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Spectral Radii of Operators and High-Power Operator Inequalities
... of operators on a Hilbert space, we present new high-power operator inequalities, and their corresponding operator in- equalities involving spectral radii of ...Halmos’ two operator inequalities, ...
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Spectral theory of Schrödinger operators and the almost Mathieu operator
... Quantum mechanics is basically about solving the Schr¨ odinger equation. The Schr¨ odinger equation is the most fundamental equation in quantum mechanics. The n-dimensional Schr¨ odinger equation is defined as i~ δΨ δt = ...
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Inverse spectral problems for Dirac operators on a finite interval
... inverse spectral problems for Dirac operators with potentials from different classes have been ...Dirac operators on a finite interval with continuous potentials were considered in [3,4] (recon- ...
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Spectral properties of integrable Schrodinger operators with singular potentials
... Another interesting direction for future research is the difference case, where we believe the answer will depend on the arithmetic properties of the shift η = P/Q. In the limit Q → ∞ we should recover the previous ...
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