12 citations · 30 across the 11 of their papers we have counts for
13 papers
Crofton formulae for products
Dmitri Akhiezer, Boris Kazarnovskii
It is shown how new integral-geometric formulae can be obtained from the existing formulae of Crofton type. In particular, for classical Crofton formulae in which the answer depend…
The ring of normal densities, Gelfand transform and smooth BKK-type theorems
Dmitri Akhiezer, Boris Kazarnovskii
We suggest an algorithm allowing to obtain some new integral-geometric formulae from the existing formulae of Crofton type. These new formulae are applied to get smooth versions of…
Average number of zeros and mixed symplectic volume of Finsler sets
Dmitri Akhiezer, Boris Kazarnovskii
Let be an -dimensional manifold and finite-dimensional vector spaces with Euclidean metric. We assign to each a Finsl…
An estimate for the average number of common zeros of Laplacian eigenfunctions
Dmitri Akhiezer, Boris Kazarnovskii
On a compact Riemannian manifold of dimension , we consider eigenfunctions of the Laplace operator with eigenvalue . If is homogeneous under a compact Lie gro…
On common zeros of eigenfunctions of the Laplace operator
Dmitri Akhiezer, Boris Kazarnovskii
We consider the eigenfunctions of the Laplace operator on a compact Riemannian manifold of dimension . For homogeneous with irreducible isotropy representation and for a…
On the commutator map for real semisimple Lie algebras
Dmitri Akhiezer
We find new sufficient conditions for the commutator map of a real semisimple Lie algebra to be surjective. As an application we prove the surjectivity of the commutator map for al…