activity
20082024
most citedTime-dependent Schrödinger perturbations of transition densities

12 citations · 35 across the 19 of their papers we have counts for

collaborators

25 papers

math.AP2024

Hardy perturbations of subordinated Bessel heat kernels

Krzysztof Bogdan, Tomasz Jakubowski, Konstantin Merz

Motivated by the spectral theory of relativistic atoms, we prove matching upper and lower bounds for the transition density of Hardy perturbations of subordinated Bessel heat kerne…

math.AP2022

Estimates of gradient of -harmonic functions for nonlocal operators with order

Tomasz Grzywny, Tomasz Jakubowski, Grzegorz Żurek

We obtain Grönwall type estimates for the gradient of the harmonic functions for a Lévy operator with order strictly larger than 1 and minimal assumptions of its Lévy measure.

math.AP2022

Relativistic stable operators with critical potentials

Tomasz Jakubowski, Kamil Kaleta, Karol Szczypkowski

We give local in time sharp two sided estimates of the heat kernel associated with the relativistic stable operator perturbed by a critical (Hardy) potential.

math.FA2022★ 3 cited

Bound states and heat kernels for fractional-type Schrödinger operators with singular potentials

Tomasz Jakubowski, Kamil Kaleta, Karol Szczypkowski

We consider non-local Schrödinger operators in , , where the kinetic terms are pseudo-differential operators which are perturbations of th…

math.AP2022

Fractional Burgers equation with singular initial condition

Tomasz Jakubowski, Grzegorz Serafin

We consider the fractional Burgers equation on , , with { and} and prove the existence of a s…

math.AP2022

Ground-state representation for fractional Laplacian on half-line

Tomasz Jakubowski, Paweł Maciocha

We give ground-state representation for the fractional Laplacian with Dirichlet condition on the half-line