Search for dissertations about: "Hilbert series"

Showing result 1 - 5 of 20 swedish dissertations containing the words Hilbert series.

  1. 1. Around minimal Hilbert series problems for graded algebras

    Author : Lisa Nicklasson; Samuel Lundqvist; Christian Gottlieb; Uwe Nagel; Stockholms universitet; []
    Keywords : NATURAL SCIENCES; NATURVETENSKAP; NATURVETENSKAP; NATURAL SCIENCES; Graded algebras; Hilbert series; Lefschetz properties; Exterior algebra; Linear resolution; matematik; Mathematics;

    Abstract : The Hilbert series of a graded algebra is an invariant that encodes the dimension of the algebra's graded compontents. It can be seen as a tool for measuring the size of a graded algebra. This gives rise to the idea of algebras with a "minimal Hilbert series", among the algebras within a certain family. READ MORE

  2. 2. Tangential Derivations, Hilbert Series and Modules over Lie Algebroids

    Author : Yohannes Tadesse; Rolf Källström; Michael Granger; Stockholms universitet; []
    Keywords : NATURAL SCIENCES; NATURVETENSKAP; NATURVETENSKAP; NATURAL SCIENCES; Tangential Derivations; Monomials; Multiplier Ideals; Lie Algebroids; Hilbert series; matematik; Mathematics;

    Abstract : Let A/k be a local commutative algebra over a field k of characteristic 0, and T_{A/k} be the module of k-linear derivations on A. We study, in two papers, the set of k-linear derivations on A which are tangential to an ideal I of A (preserves I), defining an A-submodule T_{A/k}(I) of T_{A/k}, which moreover is a k-Lie subalgebra. READ MORE

  3. 3. Waring-type problems for polynomials : Algebra meets Geometry

    Author : Alessandro Oneto; Boris Shapiro; Brian Harbourne; Stockholms universitet; []
    Keywords : NATURAL SCIENCES; NATURVETENSKAP; NATURVETENSKAP; NATURAL SCIENCES; polynomials; Waring problems; Hilbert series; fat points; power ideals; secant varieties; matematik; Mathematics;

    Abstract : In the present thesis we analyze different types of additive decompositions of homogeneous polynomials. These problems are usually called Waring-type problems and their story go back to the mid-19th century and, recently, they received the attention of a large community of mathematicians and engineers due to several applications. READ MORE

  4. 4. Hilbert space frames and bases : a comparison of Gabor and wavelet frames and applications to multicarrier digital communications

    Author : Niklas Grip; Luleå tekniska universitet; []
    Keywords : NATURAL SCIENCES; NATURVETENSKAP; NATURVETENSKAP; NATURAL SCIENCES; Mathematics; Matematik;

    Abstract : Several signal processing applications today are based on the use of different transforms. The signals under consideration are written as a linear combination (or series) of some predefined set of functions. Traditionally, orthogonal bases have been used for this purpose, for example, in the discrete Fourier transform. READ MORE

  5. 5. Infinite dimensional holomorphy in the ring of formal power series : partial differential operators

    Author : Henrik Petersson; Andrei Khrennikov; Sean Dineen; Växjö universitet; []
    Keywords : NATURAL SCIENCES; NATURVETENSKAP; Infinite dimensional holomorphy; Formal power series; Fourier-Borel transform; Paley-Wiener theorem; Fischer decomposition; Fischer pair; Fock space; Cauchy-Problem; Kergin operator; PDE-preserving; Pseudo-differential operators.; MATHEMATICS; MATEMATIK;

    Abstract : We study holomorphy in the ring of formal power series in an infinite number of variables. Thus we restrict our study to (infinite dimensional) holomorphy on sequence spaces and we show that we obtain a rich theory without requiring any topological structure on the domain space. We make a comprehensive PDO-study for the spaces under consideration. READ MORE