2 citations · 4 across the 7 of their papers we have counts for
9 papers
Idempotents in nonassociative algebras and eigenvectors of quadratic operators
Yuri Lyubich, Alexander Tsukerman
Let be a field, char. Then every finite-dimensional -algebra has either an idempotent or an absolute nilpotent if and only if over every polynomial of odd deg…
A recursive construction of projective cubature formulas and related isometric embeddings
Yuri I. Lyubich, Oksana A. Shatalova
A recursive construction is presented for the projective cubature formulas of index on the unit spheres where is or , or . This yields a lot o…
The cohomological equations in nonsmooth categories
Yu. I. Lyubich
The functional equation is considered in topological, measurable and related categories from the point of view of functional analysis and general theory of dy…
Geometric, spectral and asymptotic properties of averaged products of projections in Banach spaces
Catalin Badea, Yuri I. Lyubich
According to the von Neumann-Halperin and Lapidus theorems, in a Hilbert space the iterates of products or, respectively, of convex combinations of orthoprojections are strongly co…
Upper bound for isometric embeddings \ell_2^m\to\ell_p^n
Yuri I. Lyubich
The isometric embeddings (, ) over a field are considered, and an upper bound for the minimal is proved. In the…
Axiomatic theory of divergent series and cohomological equations
Yuri I. Lyubich
A general theory of summation of divergent series based on the Hardy-Kolmogorov axioms is developed. A class of functional series is investigated by means of ergodic theory. The re…
Lower bounds for projective designs, cubature formulas and related isometric embeddings
Yuri Lyubich
Yudin's lower bound for the spherical designs is generalized to the cubature formulas on the projective spaces over a field K, where K can be R, C, or H (the field of quaternions),…
On tight projective designs
Yuri I. Lyubich
It is shown that among all tight designs in FP^n, where F is R, C, or H (quaternions), other than RP^1, only 5-designs in CP^1 have irrational angle set. This is the only case of e…
A new advance in the Bernstein problem in mathematical genetics
Yuri I. Lyubich
A S. N. Bernstein problem is solved under a natural irreducibility condition. Earlier this result was obtained only in some special case.