Zobrazeno 1 - 10
of 146
pro vyhledávání: '"Greenleaf, Allan"'
The study of the asymptotics of the spectral function for self-adjoint, elliptic differential, or more generally pseudodifferential, operators on a compact manifold has a long history. The seminal 1968 paper of H\"ormander, following important prior
Externí odkaz:
http://arxiv.org/abs/2411.10401
Let $\phi(x,y)$ be a continuous function, smooth away from the diagonal, such that, for some $\alpha>0$, the associated generalized Radon transforms \begin{equation} \label{Radon} R_t^{\phi}f(x)=\int_{\phi(x,y)=t} f(y) \psi(y) d\sigma_{x,t}(y) \end{e
Externí odkaz:
http://arxiv.org/abs/2401.11597
We introduce a class of Falconer distance problems, which we call of restricted type, lying between the classical version and its pinned variant. Prototypical restricted distance sets are the diagonal distance sets, $k$-point configuration sets given
Externí odkaz:
http://arxiv.org/abs/2305.18053
We prove new results of Mattila-Sj\"olin type, giving lower bounds on Hausdorff dimensions of thin sets $E\subset \Bbb R^d$ ensuring that various $k$-point configuration sets, generated by elements of $E$, have nonempty interior. The dimensional thre
Externí odkaz:
http://arxiv.org/abs/2209.02084
Publikováno v:
Inverse Prob. and Imaging 16 (2022), no. 6, 1543-1570
Borehole seismic data is obtained by receivers located in a well, with sources located on the surface or in another well. Using microlocal analysis, we study possible approximate reconstruction via linearized, filtered backprojection of an isotropic
Externí odkaz:
http://arxiv.org/abs/2110.01682
Publikováno v:
Mathematika 68 (2022), no. 1, 163-190
We give conditions for $k$-point configuration sets of thin sets to have nonempty interior, applicable to a wide variety of configurations. This is a continuation of our earlier work \cite{GIT19} on 2-point configurations, extending a theorem of Matt
Externí odkaz:
http://arxiv.org/abs/2005.10796
Publikováno v:
Jour. Geometric Analysis 31 (2021), no. 7, 6662-6680
A theorem of Steinhaus states that if $E\subset \mathbb R^d$ has positive Lebesgue measure, then the difference set $E-E$ contains a neighborhood of $0$. Similarly, if $E$ merely has Hausdorff dimension $\dim_{\mathcal H}(E)>(d+1)/2$, a result of Mat
Externí odkaz:
http://arxiv.org/abs/1907.12513
Publikováno v:
Math. Zeitschrift 297 (2021), 855-865
We prove the existence of similar and multi-similar point configurations (or simplexes) in sets of fractional Hausdorff measure in Euclidean space. These results can be viewed as variants, for thin sets, of theorems for sets of positive density in $\
Externí odkaz:
http://arxiv.org/abs/1808.04290
Publikováno v:
Inverse Prob. and Imaging, 13-6 (2019), 1283-1307
We study the existence and suppression of artifacts for a Doppler-based Synthetic Aperture Radar (DSAR) system. The idealized air- or space-borne system transmits a continuous wave at a fixed frequency and a co-located receiver measures the resulting
Externí odkaz:
http://arxiv.org/abs/1805.12483
Let $\sigma$ be arc-length measure on $S^1\subset \mathbb R^2$ and $\Theta$ denote rotation by an angle $\theta \in (0, \pi]$. Define a model bilinear generalized Radon transform, $$B_{\theta}(f,g)(x)=\int_{S^1} f(x-y)g(x-\Theta y)\, d\sigma(y),$$ an
Externí odkaz:
http://arxiv.org/abs/1704.00861