Search results for "Stanley symmetric function"

showing 3 items of 3 documents

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.

Pure mathematicsTriple systemGeneral MathematicsFreudenthal magic squareElementary symmetric polynomialStanley symmetric functionComplete homogeneous symmetric polynomialRing of symmetric functionsAlgorithmSymmetric closureMathematicsAnalytic functionProceedings of the Edinburgh Mathematical Society
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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.

Power sum symmetric polynomialTriple systemGeneral Mathematics010102 general mathematicsSubalgebraStanley symmetric functionComplete homogeneous symmetric polynomial01 natural sciences010101 applied mathematicsAlgebraSymmetric polynomialComputingMethodologies_DOCUMENTANDTEXTPROCESSINGElementary symmetric polynomial0101 mathematicsRing of symmetric functionsMathematicsProceedings of the Royal Society of Edinburgh: Section A Mathematics
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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.

Discrete mathematicsPower sum symmetric polynomialTriple systemSpectra of algebrasApplied MathematicsSymmetric polynomialsStanley symmetric functionComplete homogeneous symmetric polynomialSymmetric convolutionSymmetric functionEntire functions of exponential typeElementary symmetric polynomialRing of symmetric functionsPolynomials and analytic functions on Banach spacesAnalysisMathematicsJournal of Mathematical Analysis and Applications
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