Search results for "Partition of unity"

showing 3 items of 3 documents

Smooth Feshbach map and operator-theoretic renormalization group methods

2003

Abstract A new variant of the isospectral Feshbach map defined on operators in Hilbert space is presented. It is constructed with the help of a smooth partition of unity, instead of projections, and is therefore called smooth Feshbach map . It is an effective tool in spectral and singular perturbation theory. As an illustration of its power, a novel operator-theoretic renormalization group method is described and applied to analyze a general class of Hamiltonians on Fock space. The main advantage of the new renormalization group method over its predecessors is its technical simplicity, which it owes to the use of the smooth Feshbach map.

Singular perturbationClass (set theory)010102 general mathematicsMathematical analysisHilbert spaceRenormalization group01 natural sciencesFock spacesymbols.namesakeIsospectralPartition of unity0103 physical sciencessymbolsFunctional renormalization group010307 mathematical physics0101 mathematicsAnalysisMathematical physicsMathematicsJournal of Functional Analysis
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A Riemann-Type Integral on a Measure Space

2005

In a compact Hausdorff measure space we define an integral by partitions of the unity and prove that it is nonabsolutely convergent.

Lebesgue measureMathematical analysisMeasure (physics)Mathematics::General Topologypartition of unityRiemann integralRiemann–Stieltjes integralLebesgue integration$PU^*$-integralsymbols.namesakeTransverse measureDifferentiation of integralssymbolsGeometry and TopologyDaniell integral28A25Borel measureAnalysisMathematicsReal Analysis Exchange
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A note on quarkonial systems and multilevel partition of unity methods

2013

We discuss the connection between the theory of quarkonial decompositions for function spaces developed by Hans Triebel, and the multilevel partition of unity method. The central result is an alternative approach to the stability of quarkonial decompositions in Besov spaces , s > n(1/p − 1)+, which leads to relaxed decay assumptions on the elements of a quarkonial system as the monomial degree grows.

AlgebraMonomialPure mathematicsDegree (graph theory)Partition of unityFunction spaceGeneral MathematicsBernstein inequalitiesStability (probability)Connection (mathematics)MathematicsMathematische Nachrichten
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