Search results for "symmetric functions"
showing 7 items of 7 documents
Degrees of irreducible characters of the symmetric group and exponential growth
2015
We consider sequences of degrees of ordinary irreducible S n S_n - characters. We assume that the corresponding Young diagrams have rows and columns bounded by some linear function of n n with leading coefficient less than one. We show that any such sequence has at least exponential growth and we compute an explicit bound.
Computing with Rational Symmetric Functions and Applications to Invariant Theory and PI-algebras
2012
The research of the first named author was partially supported by INdAM. The research of the second, third, and fourth named authors was partially supported by Grant for Bilateral Scientific Cooperation between Bulgaria and Ukraine. The research of the fifth named author was partially supported by NSF Grant DMS-1016086.
2-SYMMETRIC CRITICAL POINT THEOREMS FOR NON-DIFFERENTIABLE FUNCTIONS
2008
AbstractIn this paper, some min–max theorems for even andC1functionals established by Ghoussoub are extended to the case of functionals that are the sum of a locally Lipschitz continuous, even term and a convex, proper, lower semi-continuous, even function. A class of non-smooth functionals admitting an unbounded sequence of critical values is also pointed out.
The convolution operation on the spectra of algebras of symmetric analytic functions
2012
Abstract We show that the spectrum of the algebra of bounded symmetric analytic functions on l p , 1 ≤ p + ∞ with the symmetric convolution operation is a commutative semigroup with the cancellation law for which we discuss the existence of inverses. For p = 1 , a representation of the spectrum in terms of entire functions of exponential type is obtained which allows us to determine the invertible elements.
The algebra of symmetric analytic functions on L∞
2017
We consider the algebra of holomorphic functions on L∞ that are symmetric, i.e. that are invariant under composition of the variable with any measure-preserving bijection of [0, 1]. Its spectrum is identified with the collection of scalar sequences such that is bounded and turns to be separable. All this follows from our main result that the subalgebra of symmetric polynomials on L∞ has a natural algebraic basis.
Elementary symmetric functions of two solvents of a quadratic matrix equations
2008
Quadratic matrix equations occur in a variety of applications. In this paper we introduce new permutationally invariant functions of two solvents of the n quadratic matrix equation X^2- L1X - L0 = 0, playing the role of the two elementary symmetric functions of the two roots of a quadratic scalar equation. Our results rely on the connection existing between the QME and the theory of linear second order difference equations with noncommutative coefficients. An application of our results to a simple physical problem is briefly discussed.
Some algebras of symmetric analytic functions and their spectra
2011
AbstractIn the spectrum of the algebra of symmetric analytic functions of bounded type on ℓp, 1 ≤ p < +∞, and along the same lines as the general non-symmetric case, we define and study a convolution operation and give a formula for the ‘radius’ function. It is also proved that the algebra of analytic functions of bounded type on ℓ1 is isometrically isomorphic to an algebra of symmetric analytic functions on a polydisc of ℓ1. We also consider the existence of algebraic projections between algebras of symmetric polynomials and the corresponding subspace of subsymmetric polynomials.