One of the leading problems of algebraic complexity theory is matrix multiplication. The näıve multiplication of two n× n matrices uses n multiplications. In 1969 Strassen [19] presented an explicit algorithm for multiplying 2 × 2 matrices using seven multiplications. In the opposite direction, Hopcroft and Kerr [11] and Winograd [20] proved independently that there is no algorithm for multiply...

We exhibit a vertex operator which implements multiplication by power-sums of Jucys-Murphy elements in the centers of the group algebras of all symmetric groups simultaneously. The coefficients of this operator generate a representation of W1+∞, to which operators multiplying by normalized conjugacy classes are also shown to belong. A new derivation of such operators based on matrix integrals i...

The paper deals with twistor spinors on Lorentzian manifolds. In particular , we explain a relation between a certain class of Lorentzian twistor spinors and the Feeerman spaces of strictly pseudoconvex spin manifolds which appear in CR-geometry. Let (M n;k ; g) be a n-dimensional smooth semi-Riemannian spin manifold of index k with the spinor bundle S. There are two conformally covariant diffe...

hold with some constant C independent of f? (Unless otherwise specified, all integrals are taken with respect to the standard Lebesgue measure on R.) Denoting w := u−1, we can reformulate the above question as follows: When is the operator T := M√vT0M√w bounded in L ? (Here Mφ stands for the operator of multiplication by φ.) Such weighted norm inequalities arise naturally in many areas of analy...

We define a class of probabilistic models in terms of an operator algebra of stochastic processes, and a representation for this class in terms of stochastic parameterized grammars. A syntactic specification of a grammar is mapped to semantics given in terms of a ring of operators, so that grammatical composition corresponds to operator addition or multiplication. The operators are generators f...

We exhibit a vertex operator which implements multiplication by power-sums of Jucys-Murphy elements in the centers of the group algebras of all symmetric groups simultaneously. The coefficients of this operator generate a representation of W1+∞, to which operators multiplying by normalized conjugacy classes are also shown to belong. A new derivation of such operators based on matrix integrals i...

In this paper, we study spectral decompositions with respect to a system of generalized eigenvectors second-order differential operators on an interval whose resolvents possess convolution representations. We obtain the representation integral boundary conditions. Then, using generated by initial operator, construct Fourier transform. A connection between operation in original functional space ...

The paper is devoted to the study of Markov processes in finite-dimensional convex cones (especially R and R+) with a decomposable generator, i.e. with a generator of the form L = ∑N n=1Anψn, where An are operators of multiplication on continuous positive functions an(x) (which could be unbounded) and ψn are generators of the Lévy processes (or processes with i.i.d. increments) in R. The follow...