115 citations · 1.9k across the 226 of their papers we have counts for
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Determinants and Plemelj-Smithies formulas
Duván Cardona, Julio Delgado, Michael Ruzhansky
We establish Plemelj-Smithies formulas for determinants in different algebras of operators. In particular we define a Poincaré type determinant for operators on the torus $\Tn$ and…
Principal frequency of p-sub-Laplacians for general vector fields
Michael Ruzhansky, Bolys Sabitbek, Durvudkhan Suragan
In this paper, we prove the uniqueness and simplicity of the principal frequency (or the first eigenvalue) of the Dirichlet p-sub-Laplacian for general vector fields. As a byproduc…
Subelliptic pseudo-differential operators and Fourier integral operators on compact Lie groups
Duván Cardona, Michael Ruzhansky
In this memoir we extend the theory of global pseudo-differential operators to the setting of arbitrary sub-Riemannian structures on a compact Lie group. More precisely, given a co…
Subelliptic Wave Equations with Log-Lipschitz coefficients
Carlos Andres Rodriguez Torijano, Michael Ruzhansky
In this paper we study the Cauchy problem for the wave equations for sums of squares of left invariant vector fields on compact Lie groups and also for hypoelliptic homogeneous lef…
Sobolev, Hardy, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg type inequalities for some fractional derivatives
Aidyn Kassymov, Michael Ruzhansky, Niyaz Tokmagambetov +1
In this paper we show different inequalities for fractional order differential operators. In particular, the Sobolev, Hardy, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg type…
Rayleigh-Faber-Krahn, Lyapunov and Hartmann-Wintner inequalities for fractional elliptic problems
Aidyn Kassymov, Michael Ruzhansky, Berikbol T. Torebek
In this paper in the cylindrical domain we consider a fractional elliptic operator with Dirichlet conditions. We prove, that the first eigenvalue of the fractional elliptic operato…