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Generalized eigenfunctions and a Borel Theorem on the Sierpinski Gasket
Generalized eigenfunctions Borel Theorem Sierpinski Gasket
2015/12/10
There is a well developed theory (see [5, 9]) of analysis on certain types of fractal sets, of which the Sierpinski Gasket (SG) is the simplest non-trivial example. In this theory the fractals are vie...
SZEGO LIMIT THEOREMS ON THE SIERPINSKI GASKET
Analysis on Fractals equally distributed sequences Laplacian localized eigenfunctions Sierpinski gasket strong Szego limit theorem
2015/12/10
We use the existence of localized eigenfunctions of the Laplacian on the Sierpinski gasket (SG) to formulate and prove analogues of the strong Szego limit theorem in this fractal setting.Furthermore, ...
ORTHOGONAL POLYNOMIALS ON THE SIERPINSKI GASKET
Jacobi matrix Laplacian Sierpinski Gasket Orthogonal Polynomials Recursion Relation
2015/12/10
The construction of a Laplacian on a class of fractals which includes the Sierpinski gasket (SG) has given rise to an intensive research on analysis on fractals. For instance, a complete theory of pol...
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 conformal loop ensemble CLE_kappa is the canonical conformally invariant probability measure on non-crossing loops in a proper simply connected domain in the complex plane. The parameter kappa var...
Mean value properties of harmonic functions on Sierpinski gasket type fractals
Sierpinski gasket Laplacian harmonic function mean value property analysis on fractals
2012/6/27
In this paper, we establish an analogue of the classical mean value property for both the harmonic functions and some general functions in the domain of the Laplacian on the Sierpinski gasket. Further...
Exact spectrum of the Laplacian on a domain in the Sierpinski gasket
Sierpinski gasket Laplacian eigenvalues spectral decimation analysis on fractals
2012/6/27
For a certain domain $\Omega$ in the Sierpinski gasket $\mathcal{SG}$ whose boundary is a line segment, a complete description of the eigenvalues of the Laplacian under the Dirichlet and Neumann bound...
In this article we classi¯ed the points of the well-known fractal
set Sierpinski Gasket (SG) according to their addresses. We also gave a
characterization of points of SG that describes the rel...
A GRAIN OF DUST FALLING THROUGH A SIERPINSKI GASKET
Binomial random variables fractals Hausdorff dimension random walks self-similarity
2007/12/12
In this paper we analyze the downward random motion of a particle in a vertical, bounded, Sierpinski gasket $G$, where at each layer either absorption or delays are considered. In the case of motion w...