Orthogonal quadruple systems and 3-frames

Orthogonal Frames of Translates

Two Bessel sequences are orthogonal if the composition of the synthesis operator of one sequence with the analysis operator of the other sequence is the 0 operator. We characterize when two Bessel sequences are orthogonal when the Bessel sequences have the form of translates of a finite number of functions in L(R). The characterizations are applied to Bessel sequences which have an affine struc...

On Almost Orthogonal Frames

A pair of orthogonal frames

We start with a characterization of a pair of frames to be orthogonal in a shift-invariant space and then give a simple construction of a pair of orthogonal shift-invariant frames. This is applied to obtain a construction of a pair of Gabor orthogonal frames as an example. This is also developed further to obtain constructions of a pair of orthogonal wavelet frames. ∗This work was supported by ...

Affine - invariant quadruple systems

Let t, v, k, λ be positive integers satisfying v > k > t. A t-(v, k, λ) design is an ordered pair (V,B), where V is a finite set of v points, B is a collection of k-subsets of V , say blocks, such that every t-subset of V occurs in exactly λ blocks in B. In what follows we simply write t-designs. A 3-(v, 4, 1) design is called a Steiner quadruple system and denoted by SQS(v). It is known that a...

On Quadruple Systems

( n — h\ 11 m — h\ I-hi I \l-hj is the number of those elements of S (I, m, n) which contain h fixed elements of E. It is known that condition (1) is not sufficient for S(l, m, n) to exist. It has been proved that no finite projective geometry exists with 7 points on every line. This implies non-existence of 5(2, 7, 43). There arises a problem of finding a necessary and sufficient condition for...