Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

We study a linear recursion with random Markov-dependent coefficients. In a “regular variation in, regular variation out” setup we show that its stationary solution has a multivariate regularly varying distribution. This extends results previously established for i.i.d. coefficients.

(1.1) an = c1an−1 + c2an−2 + · · ·+ cdan−d for all n ≥ d. For example, the Fibonacci sequence {Fn} = (0, 1, 1, 2, 3, 5, 8, . . . ) is defined by the linear recursion Fn = Fn−1+Fn−2 with initial values F0 = 0 and F1 = 1. (Often F0 is ignored, but the values F1 = F2 = 1 and the recursion force F0 = 0.) We will assume cd 6= 0 and then say the recursion has order d; this is analogous to the degree ...

For any field k and any integers m,n with 0 6 2m 6 n + 1, let Wn be the k-vector space of sequences (x0, . . . , xn), and let Hm ⊆ Wn be the subset of sequences satisfying a degree-m linear recursion, i.e. for which there exist a0, . . . , am ∈ k such that

We define multiperiodic infinite recursions and show that for such a recursion there is a finite linear recursion, the finite core, which gives almost the same type of recur-sion except for a different offset. Moreover, if we add the sequences produced by all multiperiodic infinite recursions with a given finite core, we almost obtain a multiple of the sequence associated with the finite core.

We provide a proof of a conjecture in [2] on the existence and form of linear recursions for moments of powers of the Bessel function K0.

Abstrucr-The problem considered involves estimating a two-dimensional isotropic random field given noisy observations of this field over a disk of finite radius. By expanding the field and observations in Fourier series, and exploiting the covariance structure of the resulting Fourier coefficient processes, recursions are obtained for efficiently constructing the linear least-squares estimate o...