Displaying similar documents to “An explicit formula for period determinant”

Puiseux series polynomial dynamics and iteration of complex cubic polynomials

Jan Kiwi (2006)

Annales de l’institut Fourier

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We let 𝕃 be the completion of the field of formal Puiseux series and study polynomials with coefficients in 𝕃 as dynamical systems. We give a complete description of the dynamical and parameter space of cubic polynomials in 𝕃 [ ζ ] . We show that cubic polynomial dynamics over 𝕃 and ℂ are intimately related. More precisely, we establish that some elements of 𝕃 naturally correspond to the Fourier series of analytic almost periodic functions (in the sense of Bohr) which parametrize (near infinity)...

Paradan’s wall crossing formula for partition functions and Khovanski-Pukhlikov differential operator

Arzu Boysal, Michèle Vergne (2009)

Annales de l’institut Fourier

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Let P ( s ) be a family of rational polytopes parametrized by inequations. It is known that the volume of P ( s ) is a locally polynomial function of the parameters. Similarly, the number of integral points in P ( s ) is a locally quasi-polynomial function of the parameters. Paul-Émile Paradan proved a jump formula for this function, when crossing a wall. In this article, we give an algebraic proof of this formula. Furthermore, we give a residue formula for the jump, which enables us to compute it. ...

Polynomial bounds for the oscillation of solutions of Fuchsian systems

Gal Binyamini, Sergei Yakovenko (2009)

Annales de l’institut Fourier

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We study the problem of placing effective upper bounds for the number of zeroes of solutions of Fuchsian systems on the Riemann sphere. The principal result is an explicit (non-uniform) upper bound, polynomially growing on the frontier of the class of Fuchsian systems of a given dimension n having m singular points. As a function of n , m , this bound turns out to be double exponential in the precise sense explained in the paper. As a corollary, we obtain a solution of the so-called...

Wold decomposition of the Hardy space and Blaschke products similar to a contraction

M. Stessin (1999)

Colloquium Mathematicae

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The classical Wold decomposition theorem applied to the multiplication by an inner function leads to a special decomposition of the Hardy space. In this paper we obtain norm estimates for componentwise projections associated with this decomposition. An application to operators similar to a contraction is given.