12 citations · 26 across the 12 of their papers we have counts for
13 papers
On real roots of polynomial systems of equations in the context of group theory
Boris Kazarnovskii
The probability that a zero of a random real polynomial of increasing degree is real tends to zero. However, passing from polynomials to Laurent polynomials yields a surprising res…
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…
Ring of conditions for affine space
Boris Kazarnovskii
The exponential sum (ES) is a linear combination of characters of an additive group . The exponential analytic set (EAS) is a set of common zeroes of a finite tuple of…
Average number of solutions
Boris Kazarnovskii
Let be an -dimensional manifold and finite-dimensional vector spaces. For systems of equations $\{f_i = a_i\colon\: f_i\in V_i,…
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…
Mixed Hermitian volume and number of common zeros of holomorphic functions
Boris Kazarnovskii
Let be a finite dimensional Hermitian vector space of holomorphic sections of a line bundle on a complex -dimensional manifold . We associate to the non-neg…
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…
Newton polyhedra, tropical geometry and the ring of condition for
Boris Kazarnovskii, Askold Khovanskii
The ring of conditions defined by C. De Concini and C. Procesi is an intersection theory for algebraic cycles in a spherical homogeneous space. In the paper we consider the ring of…
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 product of cocycles in a polyhedral complex
B. Kazarnovskii
A product of cochains in a polyhedral complex is constructed. The multiplication algorithm depends on the choice of a parameter. The parameter is a linear functional on the ambient…
Exponential tropical varieties and complex Monge-Ampere operator
Boris Kazarnovskii
Sometimes it is possible to extend some using Newton polyhedra computations in algebraic geometry from polynomials to exponential sums. For this purpose it is useful to consider an…
On piecewise pluriharmonic functions
Boris Kazarnovskii
We extend some results on piecewise linear functions on $\C^n$ to piecewise pluriharmonic functions on any complex manifold. We construct a ring generated by currents and $dd^c…