Displaying similar documents to “Positive polynomials and hyperdeterminants”

On the Jacobian ideal of the binary discriminant.

Carlos D'Andrea, Jaydeep Chipalkatti (2007)

Collectanea Mathematica

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Let Δ denote the discriminant of the generic binary -ic. We show that for d ≥ 3, the Jacobian ideal of Δ is perfect of height 2. Moreover we describe its SL-equivariant minimal resolution and the associated differential equations satisfied by Δ. A similar result is proved for the resultant of two forms of orders , whenever ≥ -1. If Φ denotes the locus of binary forms with total root multiplicity ≥ -n, then we show that the ideal of Φ is also perfect, and we construct a covariant which...

Ultrasymmetric sequence spaces in approximation theory.

Evgeniy Pustylnik (2006)

Collectanea Mathematica

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Let φ(t) be a positive increasing function and let Ê be an arbitrary sequence space, rearrangement-invariant with respect to the atomic measure µ(n) = 1/n. Let {a*} mean the decreasing rearrangement of a sequence {|a|}. A sequence space l with symmetric (quasi)norm || {φ(n)a*} || is called , because it is not only intermediate but also interpolation between the corresponding Lorentz and Marcinkiewicz spaces Λ and M. We study properties of the spaces l for all admissible parameters φ,...

Wiener amalgam spaces for the fundamental identity of Gabor analysis.

Hans G. Feichtinger, Franz Luef (2006)

Collectanea Mathematica

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In the last decade it has become clear that one of the central themes within Gabor analysis (with respect to general time-frequency lattices) is a duality theory for Gabor frames, including the Wexler-Raz biorthogonality condition, the Ron-Shen duality principle and the Janssen representation of a Gabor frame operator. All these results are closely connected with the so-called , which we derive from an application of Poisson's summation formula for the symplectic Fourier transform. The...

A generalization of the Nikodym boundedness theorem.

Christopher Stuart (2007)

Collectanea Mathematica

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In this note an internal property of a ring of sets, named the Nested Partition Property, is shown to imply the Nikodym Property. A wide range of examples are shown to have this property.