Krzysztof Stempak

activity

20202025

most citedFinite reflection groups and symmetric extensions of Laplacian

5 citations · 5 across the 6 of their papers we have counts for

collaborators

6 papers

math.FA2025

Self-adjoint realization of the harmonic oscillator in polar coordinates and some consequences

Krzysztof Stempak

We consider spectral decomposition of the harmonic oscillator in $R^{n}$ in terms of two different orthonormal bases in $L^{2} (R^{n})$ consisting of its eigenfunctions. T…

math.FA2025

A transform for the Grushin operator with applications

Krzysztof Stempak

In the setting of the Grushin differential operator $G = - Δ_{x^{'}} - ∣ x^{'} ∣^{2} Δ_{x^{''}}$ with domain $Dom G = C_{c}^{\infty} (R^{d}) \subset L^{2} (R^{d})$ , we define a scalar trans…

math.FA2025

Spectral analysis of Grushin type operators on the quarter plane

Krzysztof Stempak

We investigate spectral properties of self-adjoint extensions of the operator $$ G_{α,β}=-\Big(\frac{\partial^2}{\partial r^2}+\frac{2\a+1}{r}\frac{\partial}{\partial r} \Big) -r^2…

math.CA2024

Variation of the one-dimensional centered maximal operator on simple functions with gaps between pieces

Paul Hagelstein, Dariusz Kosz, Krzysztof Stempak

Let $M$ denote the centered Hardy--Littlewood operator on $R$ . We prove that \[ {\rm Var} (Mf)\le {\rm Var} (f) - \frac12\big| |f(\infty)|-|f(-\infty)|\big| \] for piecewi…

math.AP2024

Genuinely sharp estimates for heat kernels on Weyl chambers

Krzysztof Stempak

We consider heat kernels on Weyl chambers corresponding to Laplacians subject to mixed Dirichlet-Neumann boundary conditions imposed on the boundary. Using purely analytic tools we…

math.FA2020★ 5 cited

Finite reflection groups and symmetric extensions of Laplacian

Krzysztof Stempak

Let $W$ be a finite reflection group associated with a root system $R$ in $R^{d}$ . Let $C_{+}$ denote a positive Weyl chamber. Consider an open subset $Ω$ of $R^{d}$ , sym…