Zobrazeno 1 - 8
of 8
pro vyhledávání: '"Dewan, Utsav"'
Let $M$ be an $n$-dimensional Hadamard manifold of pinched negative curvature $-b^2 \leq K_M \leq -a^2$. The solution of the Dirichlet problem at infinity for $M$ leads to the construction of a family of mutually absolutely continuous probability mea
Externí odkaz:
http://arxiv.org/abs/2408.06098
Autor:
Dewan, Utsav
One of the most celebrated problems in Euclidean Harmonic analysis is the Carleson's problem: determining the optimal regularity of the initial condition $f$ of the Schr\"odinger equation given by \begin{equation*}\begin{cases} i\frac{\partial u}{\pa
Externí odkaz:
http://arxiv.org/abs/2407.13736
Autor:
Dewan, Utsav
By the classical Fatou-Kato Theorem, it is well-known that positive solutions of the Heat equation on the Euclidean upper half-space $\R^{n+1}_+$, admit finite normal limit at almost every point on the boundary $\R^n$. Watson estimated the size of th
Externí odkaz:
http://arxiv.org/abs/2311.14051
Autor:
Dewan, Utsav
By classical Fatou type theorems in various setups, it is well-known that positive harmonic functions have non-tangential limit at almost every point on the boundary. In this paper, in the setting of non-positively curved Harmonic manifolds of purely
Externí odkaz:
http://arxiv.org/abs/2309.05661
Autor:
Biswas, Kingshook, Dewan, Utsav
A well studied classical problem is the harmonicity of functions satisfying the restricted mean-value property (RMVP). While this has so far been studied mainly for domains in $\mathbb{R}^n$, we consider this problem in the general setting of domains
Externí odkaz:
http://arxiv.org/abs/2307.05215
Autor:
Bhowmik, Mithun, Dewan, Utsav
We prove $L^p-L^{p^\prime}$ boundedness of spectral projections and the resolvent of the Laplace-Beltrami operator on Damek-Ricci spaces with the explicit norms in terms of the spectral parameter. To prove these results we established pointwise sharp
Externí odkaz:
http://arxiv.org/abs/2306.06875
Autor:
Dewan, Utsav
We prove a converse of Fatou type result for certain eigenfunctions of the Lalplace-Beltrami operator on Harmonic NA groups relating sectorial convergence and admissible convergence of Poisson type integrals of complex (signed) measures. This result
Externí odkaz:
http://arxiv.org/abs/2206.08142
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