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SOME SPECTRAL PROPERTIES OF PSEUDO-DIFFERENTIAL OPERATORS ON THE SIERPINSKI GASKET
Analysis on fractals localized eigenfunctions Sierpiński gasket Szego limit theorem
2015/12/10
We prove versions of the strong Szëgo limit theorem for certain classes of pseudodifferential operators defined on the Sierpiński gasket. Ourresults used in a fundamental way the existence of loc...
THE NONCOMMUTATIVE WIENER LEMMA,LINEAR INDEPENDENCE,AND SPECTRAL PROPERTIES OF THE ALGEBRA OF TIME-FREQUENCY SHIFT OPERATORS
NONCOMMUTATIVE WIENER LEMMA LINEAR INDEPENDENCE SPECTRAL PROPERTIES OF THE ALGEBRA TIME-FREQUENCY SHIFT OPERATORS
2015/9/29
In this paper we analyze the Banach *-algebra of time-frequency shifts with absolutely summable coefficients. We prove a noncommutative version of the Wiener lemma. We also construct a faithful tracia...
Structural Analysis of Laplacian Spectral Properties with Application to Electric Transmission Networks
Laplacian Spectral Properties Electric Transmission Networks Optimization and Control
2011/9/22
Abstract: The spectrum of the Laplacian matrix of a network plays a key role in a wide range of dynamical problems associated with the network, from transient stability analysis of power networks to d...
On the spectral properties of L_{+-} in three dimensions
spectral properties three dimensions Analysis of PDEs
2011/8/23
Abstract: This paper is part of the radial asymptotic stability analysis of the ground state soliton for either the cubic nonlinear Schrodinger or Klein-Gordon equations in three dimensions. We demons...
On spectral properties of the fourth order differential operator with singular coefficients
spectral properties differential operator singular coefficients
2010/11/22
A formal fourth order differential operator with a singular coefficient that is a linear combination of the Dirac delta-function and its derivatives is considered. The asymptotic behavior of spectra ...
Extremal spectral properties of Lawson tori and the Lamé equation
Lawson torus Lawson minimal surfaces extremal metric
2010/11/26
Extremal spectral properties of the Lawson tori are studied. A Law-son torus carries an extremal metric for some eigenvalue j of the Laplace-Beltrami operator. We prove that the metric on a Lawson to...
In these notes we review recent progress (and, in Section 5, we announce a new result) oncerning the statistical properties of the spectrum of Wigner random matrices.
Spectral Properties of Grain Boundaries at Small Angles of Rotation
Schr¨odinger operators eigenvalues spectral gaps
2010/12/9
We study some spectral properties of a simple two-dimensional model for small angle defects in crystals and alloys. Starting from a periodic potential V : R2 → R, we let V#(x, y) = V (x, y) in the rig...
Deterministic spectral properties of Anderson-type Hamiltonians
spectral properties Anderson-type Hamiltonians
2010/12/1
This paper concerns the deterministic spectral properties of the self-adjoint operator A! = A + V! where V! = Pn !n( · , 'n)'n on a separable Hilbert space H with a sequence {'n} H. Here ! = (!1, !2...
Bose-Einstein Condensates and spectral properties of multicomponent nonlinear Schrodinger equations
soliton solutions scattering data dimensional BEC
2010/4/1
We analyze the properties of the soliton solutions of a class of models describing one-dimensional BEC with spin F. We describe the minimal sets of scattering data which determine uniquely both the co...
On the Spectral Properties of the Regular Sturm-Liouville Problem with the Lag Argument for Which its Boundary Conditions Depends on the Spectral Parameter
Lag argument Eigenvalue Eigenfunction Asymptotic expression
2010/3/1
In this paper, the asymptotic expression of the eigenvalues and eigenfunctions of the Sturm-Liouville equation with the lag argument y''(t) + l2 y(t) + M(t)y (t - D(t)) = 0 and the spectral parameter ...