scholarly journals Gaussian bounds for the heat kernels on the ball and the simplex: classical approach

2020 ◽  
Vol 250 (3) ◽  
pp. 235-252
Author(s):  
Gerard Kerkyacharian ◽  
Pencho Petrushev ◽  
Yuan Xu
Keyword(s):  
Heat Kernels ◽  
Classical Approach ◽  
Gaussian Bounds

scholarly journals Gaussian bounds for reduced heat kernels of subelliptic operators on nilpotent Lie groups

2002 ◽  
Vol 90 (2) ◽  
pp. 251
Author(s):  
A. F. M. Ter Elst ◽  
Humberto Prado
Keyword(s):  
Magnetic Fields ◽  
Lie Groups ◽  
Functional Calculus ◽  
Heat Kernels ◽  
Riesz Transforms ◽  
Nilpotent Lie Groups ◽  
Anharmonic Oscillators ◽  
Subelliptic Operators ◽  
Gaussian Bounds ◽  
Homogeneity Property

We obtain Gaussian estimates for the kernels of the semigroups generated by a class of subelliptic operators $H$ acting on $L_p(\boldsymbol R^k)$. The class includes anharmonic oscillators and Schrödinger operators with external magnetic fields. The estimates imply an $H_\infty$-functional calculus for the operator $H$ on $L_p$ with $p \in \langle 1,\infty\rangle$ and in many cases the spectral $p$-independence. Moreover, we show for a subclass of operators satisfying a homogeneity property that the Riesz transforms of all orders are bounded.

scholarly journals Gaussian Bounds for the Weighted Heat Kernels on the Interval, Ball, and Simplex

2019 ◽  
Vol 51 (1) ◽  
pp. 73-122 ◽  
Author(s):  
Gerard Kerkyacharian ◽  
Pencho Petrushev ◽  
Yuan Xu
Keyword(s):  
Heat Kernels ◽  
Gaussian Bounds

scholarly journals Lower estimates of heat kernels for non-local Dirichlet forms on metric measure spaces

2017 ◽  
Vol 272 (8) ◽  
pp. 3311-3346 ◽  
Author(s):  
Alexander Grigor'yan ◽  
Eryan Hu ◽  
Jiaxin Hu
Keyword(s):  
Dirichlet Forms ◽  
Heat Kernels ◽  
Metric Measure Spaces ◽  
Measure Spaces ◽  
Non Local

scholarly journals Heat kernels of the discrete Laguerre operators

2021 ◽  
Vol 111 (2) ◽  
Author(s):  
Aleksey Kostenko
Keyword(s):  
Hardy Inequality ◽  
Jacobi Polynomials ◽  
Heat Kernels ◽  
The Other ◽  
Heat Semigroup ◽  
Stochastic Completeness ◽  
Markovian Semigroup ◽  
Other Hand ◽  
The One

AbstractFor the discrete Laguerre operators we compute explicitly the corresponding heat kernels by expressing them with the help of Jacobi polynomials. This enables us to show that the heat semigroup is ultracontractive and to compute the corresponding norms. On the one hand, this helps us to answer basic questions (recurrence, stochastic completeness) regarding the associated Markovian semigroup. On the other hand, we prove the analogs of the Cwiekel–Lieb–Rosenblum and the Bargmann estimates for perturbations of the Laguerre operators, as well as the optimal Hardy inequality.

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