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Dispersive and Strichartz estimates on H-type groups

Martin Del Hierro (2005)

Studia Mathematica

Our purpose is to generalize the dispersive inequalities for the wave equation on the Heisenberg group, obtained in [1], to H-type groups. On those groups we get optimal time decay for solutions to the wave equation (decay as t - p / 2 ) and the Schrödinger equation (decay as t ( 1 - p ) / 2 ), p being the dimension of the center of the group. As a corollary, we obtain the corresponding Strichartz inequalities for the wave equation, and, assuming that p > 1, for the Schrödinger equation.

Distributions of truncations of the heat kernel on the complex projective space

Nizar Demni (2014)

Annales mathématiques Blaise Pascal

Let ( U t ) t ≥ 0 be a Brownian motion valued in the complex projective space ℂ P N - 1 . Using unitary spherical harmonics of homogeneous degree zero, we derive the densities of | U t 1 | 2 and of ( | U t 1 | 2 , | U t 2 | 2 ) , and express them through Jacobi polynomials in the simplices of ℝ and ℝ 2 respectively. More generally, the distribution of ( | U t 1 | 2 , ⋯ , | U t k | 2 ) , 2 ≤ k ≤ N - 1 may be derived using the decomposition of the unitary spherical harmonics under the action of the unitary group 𝒰 ( N - k + 1 ) yet computations become tedious. We also revisit the approach initiated in [13] and based on...

Divisors, partitions and some new q-series identities

Alexander E. Patkowski (2009)

Colloquium Mathematicae

We obtain new q-series identities that have interesting interpretations in terms of divisors and partitions. We present a proof of a theorem of Z. B. Wang, R. Fokkink, and W. Fokkink, which follows as a corollary to our main q-series identity, and offer a similar result.

Double integrals on a weighted projective plane and Hilbert modular functions for ℚ (√5)

Atsuhira Nagano (2015)

Acta Arithmetica

The aim of this paper is to give an explicit extension of classical elliptic integrals to the Hilbert modular case for ℚ (√5). We study a family of Kummer surfaces corresponding to the Humbert surface of invariant 5 with two complex parameters. Our Kummer surface is given by a double covering of the weighted projective space ℙ(1:1:2) branched along a parabola and a quintic curve. The period mapping for our family is given by double integrals of an algebraic function on chambers coming from an arrangement...

Drought models based on Burr XII variables

Saralees Nadarajah, B. M. Golam Kibria (2006)

Applicationes Mathematicae

Burr distributions are some of the most versatile distributions in statistics. In this paper, a drought application is described by deriving the exact distributions of U = XY and W = X/(X+Y) when X and Y are independent Burr XII random variables. Drought data from the State of Nebraska are used.

Duplicate inverse series relations and hypergeometric evaluations with z = 1 / 4

Wenchang Chu (2002)

Bollettino dell'Unione Matematica Italiana

The Gould-Hsu (1973) inverse series relations have been systematically applied to the research of hypergeometric identities. Their duplicate version is established and used to demonstrate several terminating F 2 3 ⁢ 1 / 4 -summation formulas. Further hypergeometric evaluations with the same variable are obtained through recurrence relations.

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