All continuous translation invariant complex-valued valuations on Lebesgue measurable functions are completely classified. And all rotation spherical also

We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.

We define representations of continuous functions on infinite streams of discrete values, both in the case of discrete-valued functions, and in the case of stream-valued functions. We define also an operation of the representations of two continuous functions between streams that yields a representation of their composite. In the case of discrete-valued functions, the representatives are well-f...

The principle of representing continuous complex-valued functions by their decomposition into three positive-valued ones is proposed for the generation of complex reference functions for a joint transform correlator. Three basic approaches involving coherent and incoherent superposition of the component functions are analyzed. The potentials and limitations of the techniques are discussed.

we characterize compact composition operators on real banach spaces of complex-valued bounded lipschitz functions on metric spaces, not necessarily compact, with lipschitz involutions and determine their spectra.

It is known that the space of real valued, continuous functions C(B) over a multidimensional compact domain B ⊂ R , k ≥ 2 does not admit Haar spaces, which means that interpolation problems in finite dimensional subspaces V of C(B) may not have a solutions in C(B). The corresponding standard short and elegant proof does not apply to complex valued functions over B ⊂ C. Nevertheless, in this sit...