Countable infinity of eigenvalues of symmetric algebraic integral equation

We study the densities of the semigroup generated by the operator $- X^{2} + | Y |$ on the 3-dimensional Heisenberg group. We show that the 7th derivatives of the densities have a jump discontinuity. Outside the plane x=0 the densities are $C^{\infty}$ . We give explicit spectral decomposition of images of $- X^{2} + | Y |$ in representations.

Oscillations of anharmonic Fourier series and the wave equation.

Alain Haraux, Vilmos Komornik (1985)

Revista Matemática Iberoamericana

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In this paper we have collected some partial results on the sign of u(t,x) where u is a (sufficiently regular) solution of ⎧ u_tt + (-1)^m Δ^mu = 0 (t,x) ∈ R x Ω ⎨ ⎩ u_|Γ = ... = Δ^m-1 u_|Γ = 0 t ∈ R. These results rely on the study of a sign of almost periodic functions of a special...

Some combinatorial and probabilistic inequalities and their application to Banach space theory

Stanisław Kwapień, Carsten Schütt (1985)

Studia Mathematica

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