Krzysztof Stempak

collaborators

4 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.CA2025

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.FA2025

A transform for the Grushin operator with applications

Krzysztof Stempak

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

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_{Î±,Î²}=-\Big(\frac{\partial^2}{\partial r^2}+\frac{2\a+1}{r}\frac{\partial}{\partial r} \Big) -r…