Search Results - "Rogers, Luke G."

The resolvent kernel for PCF self-similar fractals by IONESCU, MARIUS, PEARSE, ERIN P. J., ROGERS, LUKE G., RUAN, HUO-JUN, STRICHARTZ, ROBERT S.

“…For the Laplacian \Delta defined on a p.c.f. self-similar fractal, we give an explicit formula for the resolvent kernel of the Laplacian with Dirichlet…”
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Smooth bumps, a Borel theorem and partitions of smooth functions on p.c.f. fractals by ROGERS, Luke G, STRICHARTZ, Robert S, TEPLYAEV, Alexander

“…We provide two methods for constructing smooth bump functions and for smoothly cutting off smooth functions on fractals, one using a probabilistic approach and…”
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Gradients of Laplacian eigenfunctions on the Sierpinski gasket by Degrado, Jessica L., Rogers, Luke G., Strichartz, Robert S.

“…We use spectral decimation to provide formulae for computing the harmonic tangents and gradients of Laplacian eigenfunctions on the Sierpinski Gasket. These…”
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Estimates for the resolvent kernel of the Laplacian on p.c.f. self-similar fractals and blowups by Rogers, Luke G.

“…A central issue in studying resistance forms on post-critically finite self-similar sets is the behavior of the resolvent of the Laplacian operator. The kernel…”
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The strong maximum principle for Schrödinger operators on fractals by Ionescu, Marius V., Okoudjou, Kasso A., Rogers, Luke G.

“…We prove a strong maximum principle for Schrödinger operators defined on a class of postcritically finite fractal sets and their blowups without boundary. Our…”
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Distribution theory on P.C.F. fractals by Rogers, Luke G., Strichartz, Robert S.

“…We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on…”
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Embedding convex geometries and a bound on convex dimension by Richter, Michael, Rogers, Luke G.

“…The notion of an abstract convex geometry, due to Edelman and Jamison (1984), offers an abstraction of the standard notion of convexity in a linear…”
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Derivations and Dirichlet forms on fractals by Ionescu, Marius, Rogers, Luke G., Teplyaev, Alexander

“…We study derivations and Fredholm modules on metric spaces with a local regular conservative Dirichlet form. In particular, on finitely ramified fractals, we…”
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Degree-independent Sobolev extension on locally uniform domains by Rogers, Luke G.

“…We consider the problem of constructing extensions L k p ( Ω ) → L k p ( R n ) , where L k p is the Sobolev space of functions with k derivatives in L p and Ω…”
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Unimodular Fourier multipliers for modulation spaces by Bényi, Árpád, Gröchenig, Karlheinz, Okoudjou, Kasso A., Rogers, Luke G.

“…We investigate the boundedness of unimodular Fourier multipliers on modulation spaces. Surprisingly, the multipliers with general symbol e i | ξ | α , where α…”
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ESTIMATES FOR THE RESOLVENT KERNEL OF THE LAPLACIAN ON P. C. F. SELF-SIMILAR FRACTALS AND BLOWUPS by ROGERS, LUKE G.

“…A central issue in studying resistance forms on post-critically finite self-similar sets is the behavior of the resolvent of the Laplacian operator. The kernel…”
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SOME SPECTRAL PROPERTIES OF PSEUDO-DIFFERENTIAL OPERATORS ON THE SIERPIŃSKI GASKET by IONESCU, MARIUS, OKOUDJOU, KASSO A., ROGERS, LUKE G.

“…We prove versions of the strong Szegö limit theorem for certain classes of pseudo-differential operators defined on the Sierpiński gasket. Our results use in a…”
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Geodesic interpolation on Sierpiński gaskets by Davis, Caitlin M., LeGare, Laura A., McCartan, Cory W., Rogers, Luke G.

“…We study the analogue of a convex interpolant of two sets on Sierpiński gaskets and an associated notion of measure transport. The structure of a natural…”
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Szegö Limit Theorems on the Sierpiński Gasket by Okoudjou, Kasso A., Rogers, Luke G., Strichartz, Robert S.

“…We use the existence of localized eigenfunctions of the Laplacian on the Sierpiński gasket (SG) to formulate and prove analogues of the strong Szegö limit…”
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Smooth Bumps, a Borel Theorem and Partitions of Smooth Functions on P. C. F. Fractals by Rogers, Luke G., Strichartz, Robert S., Teplyaev, Alexander

“…We provide two methods for constructing smooth bump functions and for smoothly cutting off smooth functions on fractals, one using a probabilistic approach and…”
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On a theorem of Grigor'yan, Hu and Lau by Rogers, Luke G

“…We refine a result of Grigor'yan, Hu and Lau to give a moment condition on a heat kernel which characterizes the critical exponent at which a family of Besov…”
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Some spectral properties of pseudo-differential operators on the Sierpi\'nski gasket by Marius Ionescu, Kasso A. Okoudjou, Luke G. Rogers

“…We prove versions of the strong Szegö limit theorem for certain classes of pseudo-differential operators defined on the Sierpiński gasket. Our results use in a…”
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Spectra of three-peg Hanoi towers graphs by Hungar, Brett, Mograby, Gamal, Phelps, Madison, Rogers, Luke G, Wheeler, Jonathan

“…We consider the relationship between the Laplacians on two sequences of planar graphs, one from the theory of self-similar groups and one from analysis on…”
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Sobolev Algebra Counterexamples by Coulhon, Thierry, Rogers, Luke G

“…In the Euclidean setting the Sobolev spaces $W^{\alpha,p}\cap L^\infty$ are algebras for the pointwise product when $\alpha>0$ and $p\in(1,\infty)$. This…”
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Resistance Scaling on $4N$-Carpets by Canner, Claire, Hayes, Christopher, Huang, Shinyu, Orwin, Michael, Rogers, Luke G

“…The $4N$ carpets are a class of infinitely ramified self-similar fractals with a large group of symmetries. For a $4N$-carpet $F$, let $\{F_n\}_{n \geq 0}$ be…”
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