Search results for "Hilbert's basis theorem"

showing 3 items of 3 documents

Constructive proofs of representation theorems in separable Hilbert space

1964

Discrete mathematicsHilbert's second problemPure mathematicsHilbert manifoldRiesz representation theoremApplied MathematicsGeneral MathematicsRigged Hilbert spaceCylinder set measureHilbert's basis theoremConstructivesymbols.namesakesymbolsKuiper's theoremMathematicsCommunications on Pure and Applied Mathematics
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Universal formulas for characteristic classes on the Hilbert schemes of points on surfaces

2007

This article can be seen as a sequel to the first author's article ``Chern classes of the tangent bundle on the Hilbert scheme of points on the affine plane'', where he calculates the total Chern class of the Hilbert schemes of points on the affine plane by proving a result on the existence of certain universal formulas expressing characteristic classes on the Hilbert schemes in term of Nakajima's creation operators. The purpose of this work is (at least) two-fold. First of all, we clarify the notion of ``universality'' of certain formulas about the cohomology of the Hilbert schemes by defining a universal algebra of creation operators. This helps us to reformulate and extend a lot of the f…

Hilbert manifoldHilbert's basis theoremHilbert matrix01 natural sciencesMathematics - Algebraic Geometrysymbols.namesakeCharacteristic classesPrimary 14C05Secondary 14C170103 physical sciencesFOS: Mathematics[MATH]Mathematics [math]0101 mathematicsAlgebraic Geometry (math.AG)ComputingMilieux_MISCELLANEOUSMathematicsHilbert–Poincaré seriesHilbert's second problemHilbert series and Hilbert polynomialAlgebra and Number Theory010102 general mathematicsHilbert's fourteenth problemUniversal formulasPrimary 14C05; Secondary 14C17Hilbert schemes of pointsAlgebraHilbert schemesymbols[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]010307 mathematical physics
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Rolle's Theorem for Polynomials of Degree Four in a Hilbert Space

2002

AbstractIn an infinite-dimensional real Hilbert space, we introduce a class of fourth-degree polynomials which do not satisfy Rolle's Theorem in the unit ball. Extending what happens in the finite-dimensional case, we show that every fourth-degree polynomial defined by a compact operator satisfies Rolle's Theorem.

Hilbert spacesDiscrete mathematicsHilbert manifoldRolle's theorempolynomialsApplied MathematicsHilbert spaceHilbert's basis theoremCompact operator on Hilbert spacesymbols.namesakeVon Neumann's theoremHilbert schemeRolle's TheoremsymbolsBrouwer fixed-point theoremAnalysisMathematicsJournal of Mathematical Analysis and Applications
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