In this paper a hybrid type theory HTT is deened which combines the programming language notion of partial type with the logical notion of total type into a single theory. A new partial type constructor A is added to the type theory: objects in A may diverge, but if they converge, they must be members of A. A xed point typing rule is given to allow for typing of xed points. The underlying theor...

The basics of a block oriented fractal image coder, are described. The output of the coder is an IFS (Iterated Function System) code, which describes the image as a xed-point of a contractive transformation. A new hierarchical interpretation of the IFS code, which relates diierent scales of the xed-point to the code, is presented and proved. The proof is based on nding a function of a continuou...

A frame is a family {fi}i=1 of elements in a Hilbert space H with the property that every element in H can be written as a (infinite) linear combination of the frame elements. Frame theory describes how one can choose the corresponding coefficients, which are called frame coefficients. From the mathematical point of view this is gratifying, but for applications it is a problem that the calculat...