Sökning: "orthogonal polynomials"

Visar resultat 11 - 15 av 22 avhandlingar innehållade orden orthogonal polynomials.

  1. 11. Extreme points of the Vandermonde determinant in numerical approximation, random matrix theory and financial mathematics

    Författare :Asaph Keikara Muhumuza; Sergei Silvestrov; Anatoliy Malyarenko; Karl Lundengård; Milica Rancic; Olga Liivapuu; Mälardalens högskola; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Mathematics Applied Mathematics; matematik tillämpad matematik;

    Sammanfattning : This thesis discusses the extreme points of the Vandermonde determinant on various surfaces, their applications in numerical approximation, random matrix theory and financial mathematics. Some mathematical models that employ these extreme points such as curve fitting, data smoothing, experimental design, electrostatics, risk control in finance and method for finding the extreme points on certain surfaces are demonstrated. LÄS MER

  3. 12. Fluctuations of smooth linear statistics of determinantal point processes

    Författare :Lambert Gaultier; Kurt Johansson; Igor Krasovsky; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematics; Matematik;

    Sammanfattning : We study eigenvalues of unitary invariant random matrices and other de-terminantal point processes. Paper A investigates some generalizations ofthe Gaussian Unitary Ensemble which are motivated by the physics of freefermions. LÄS MER

  4. 13. Quantum many-body systems exactly solved by special functions

    Författare :Martin Hallnäs; Edwin Langmann; Pavel Winternitz; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Quantum many-body systems; integrable systems; special functions; Mathematical physics; Matematisk fysik;

    Sammanfattning : This thesis concerns two types of quantum many-body systems in one dimension exactly solved by special functions: firstly, systems with interactions localised at points and solved by the (coordinate) Bethe ansatz; secondly, systems of Calogero-Sutherland type, as well as certain recently introduced deformations thereof, with eigenfunctions given by natural many-variable generalisations of classical (orthogonal) polynomials. The thesis is divided into two parts. LÄS MER

  5. 14. Asymptotics of Eigenpolynomials of Exactly-Solvable Operators

    Författare :Tanja Bergkvist; Boris Shapiro; Andrei Martinez-Finkelshtein; Stockholms universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; exactly-solvable; eigenpolynomials; zero distribution; asymptotics; MATHEMATICS; MATEMATIK; matematik; Mathematics;

    Sammanfattning : The main topic of this doctoral thesis is asymptotic properties of zeros in polynomial families arising as eigenfunctions to exactly-solvable differential operators. The study was initially inspired by a number of striking results from computer experiments performed by G. Masson and B. Shapiro for a more restrictive class of operators. LÄS MER

  7. 15. Hankel operators and Plancherel formula

    Författare :Genkai Zhang; Stockholms universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES;

    Sammanfattning : We consider the natural unitary action of the group SU(d, 1) on the Hilbert space L2(B,d/j,\), where B is the unit ball of C , dfi\ is the measure K(z, z)~~*+ï dm(z), and K(z, z) the reproducing kernel of the Bergman space on B. For A >—1 and not an integer, a Plancherel formula is proved for this action and, in particular, an explicit formula for the correponding Plancherel measure is found. LÄS MER