Non-Archimedean Radial Calculus: Volterra Operator and Laplace Transform

The Vladimirov–Taibleson operator: inequalities, Dirichlet problem, boundary Hölder regularity

“…A number of important results on spectral properties of D α , its perturbations and generalizations, as well as the theory of related partial (pseudo-) differential equations are covered by the monographs [1,16,34,30,36,14] and many recent papers, such as [4,2,3,17,19,20,37,33] and others.…”

The Vladimirov-Taibleson Operator: Inequalities, Dirichlet Problem, Boundary Hölder Regularity

“…A number of important results on spectral properties of D α , its perturbations and generalizations, as well as the theory of related partial (pseudo-) differential equations are covered by the monographs [1,16,34,30,36,14] and many recent papers, such as [4,2,3,17,19,20,37,33] and others.…”

$$L^p$$ properties of non-Archimedean fractional differentiation operators

“…Both the investigation of the fractional Laplacian and Vladimirov operator are far from their completion. For the latter, it is worth mentioning discoveries of such hidden structures as an isotropic Laplacian [3], oscillation properties of the corresponding heat kernel [2], integral equations resembling the classical Volterra ones connected to the restriction of D α to radial functions [10][11][12].…”