Related papers: Analysis of Schr\"odinger means
We study weighted boundedness of Hardy-Littlewood-type maximal function involving Orlicz functions. We also obtain some sufficient conditions for the weighted boundedness of the Hardy-Littlewood maximal function of the upper-half plane.
We discuss resonances for Schr\"odinger operators with compactly supported potentials on the line and the half-line. We estimate the sum of the negative power of all resonances and eigenvalues in terms of the norm of the potential and the…
This article is devoted to some foundational questions of resurgent analysis as applied to the Schr\"odinger equation in one dimension.
In this paper we establish mixed norm estimates of interactive Schr\"{o}dinger waves and apply them to study smoothing properties and global well-posedness of the nonlinear Schr\"{o}dinger equations with mass critical nonlinearity.
We present an alternative way to recover the recent result from \cite{LR} using the pseudoconformal transformation.
We define and study rational discrete analytic functions and prove the existence of a coisometric realization for discrete analytic Schur multipliers.
We study the spectral properties of a Schr\"odinger operator, in presence of a confining potential given by the distance squared from a fixed compact potential well. We prove continuity estimates on both the eigenvalues and the eigenstates,…
Motivated by a recent work of Schippa (2022), we consider local smoothing estimates for Schr\"{o}dinger equations in modulation spaces. By using the C\'{o}rdoba-Fefferman type reverse square function inequality and the bilinear Strichartz…
For functions in the Sobolev space $H^s$ and decreasing sequences $t_n\to 0$ we examine convergence almost everywhere of the generalized Schr\"odinger means on the real line, given by \[S^af(x,t_n)=\exp( it_n (-\partial_{xx})^{a/2})f(x);\]…
We analyse the exact solutions of a conditionally-solvable Schr\"odinger equation with a rational potential. From the nodes of the exact eigenfunctions we derive a connection between the otherwise isolated exact eigenvalues and the actual…
We describe the generic behavior of the resonance counting function for a Schr\"odinger operator with a bounded, compactly-supported real or complex valued potential in $d \geq 1$ dimensions. This note contains a sketch of the proof of our…
In this paper, we give an approximate formula for the measure of extreme values for the logarithm of the Riemann zeta-function and its iterated integrals. The result recovers the unconditional best result for the $\Omega$-result of…
We construct explicit integral relations between propagators of generalized Schr\"odinger equations that are linked by higher-order supersymmetry. Our results complement and extend the findings obtained in J. Phys.A 40, 10557 (2007) for the…
In this work we obtain weighted boundedness results for singular integral operators with kernels exhibiting exponential decay. We also show that the classes of weights are characterized by a suitable maximal operator. Additionally, we study…
We study Schr\"odinger operators given by positive quadratic forms on infinite graphs. From there, we develop a criticality theory for Schr\"odinger operators on general weighted graphs.
The present work aims at obtaining estimates for transformation operators for one-dimensional perturbed radial Schr\"odinger operators. It provides more details and suitable extensions to already existing results, that are needed in other…
We prove some multiplicity results for a nonlinear equation of Schroedinger type with potential functions
I point out finite propagation speed phenomena for discrete and continuous Schr\"odinger operators and discuss kernel estimates from this point of view.
Estimates of some integrals related to variations of smooth functions are presented.
We survey old and new conjectures and results on various types of spherical maximal functions, emphasizing problems with a fractal dilation set.