Note on orthonormal expansions

Minimal partial realization from generalized orthonormal basis function expansions

A solution is presented for the problem of realizing a discrete-time LTI state-space model of minimal McMillan degree such that its :rst N expansion coe;cients in terms of generalized orthonormal basis match a given sequence. The basis considered, also known as the Hambo basis, can be viewed as a generalization of the more familiar Laguerre and two-parameter Kautz constructions, allowing genera...

Orthonormal Expansions of Invariant Densities for Expanding Maps

A general transform theory of rational orthonormal basis function expansions∗

In this paper a general transform theory is presented that underlies expansions of stable discrete-time transfer functions in terms of rational orthonormal bases. The types of bases considered are generated by cascade connections of stable all-pass functions. If the all-pass sections in such a network are all equal, this gives rise to the Hambo basis construction. In this paper a more general c...

A note on some expansions of p - adic functions

Introduction. Recently J. Rutkowski (see [3]) has defined the p-adic analogue of the Walsh system, which we shall denote by (φm)m∈N0 . The system (φm)m∈N0 is defined in the space C(Zp,Cp) of Cp-valued continuous functions on Zp. J. Rutkowski has also considered some questions concerning expansions of functions from C(Zp,Cp) with respect to (φm)m∈N0 . This paper is a remark to Rutkowski’s paper....

A Note on Edgeworth Expansions for the Lattice Case

It is shown in this note that the one-term Edgeworth expansion for the standardized sample mean of n independent lattice random vectors when perturbed by a random variable (l/&)U is the same as in the strongly non-lattice case, where U is a bounded random variable depending only on a basis of the associated minimal lattice. An explicit form of U is given. Some applications to the student&d stat...