in this paper, we establish some new results in ultra bessel sequences and ultra bessel sequences of subspaces. also, we investigate ultra bessel sequences in direct sums of hilbert spaces.specially, we show that {( fi, gi)}∞ i=1 is a an ultra bessel sequencefor hilbert space h ⊕ k if and only if { fi}∞ i=1 and {gi}∞ i=1 are ultrabessel sequences for hilbert spaces h and k, respectively.

This paper explores various interfaces between the class of generalized gamma convolution (GGC) random variables, Dirichlet process mean functionals and phenomena connected to the local time and occupation time of p-skew Bessel processes and bridges discussed in Barlow, Pitman and Yor (1989), Pitman and Yor (1992, 1997b). First, some general calculus for GGC and Dirichlet process means func-tio...

We write down the generalized Bessel function associated with the root system of type D by means of multivariate hypergeometric series. Our hint comes from the particular case of the Brownian motion in the Weyl chamber of type D.