A composition operator is an operator on a space of functions defined on the same set. Its action is by composition to the right with a fixed selfmap of that set. A composition operator followed by a multiplication operator is called a weighted composition operator. In this paper, we study when weighted composition operators on the Hilbert Hardy space of the open unit disc are isometric. We fin...

We obtain a Shimorin Wold-type decomposition for doubly commuting covariant representation of product system $$C^*$$ -correspondences over $${\mathbb {N}}_0^k$$ . This result gives Shimorin-type decompositions recent by Jeu and Pinto (Adv Math 368:107–149, 2020) the q-doubly isometries Popescu (J Funct Anal 279:108798, Doubly $$\Lambda $$ -commuting row isometries. Application to wandering subs...

We develop parametric modeling and estimation methods for STAP data based on the results of the 2-D Wold-like decomposition. We show that the same parametric model that results from the 2-D Wold-like orthogonal decomposition naturally arises as the physical model in the problem of spacetime processing of airborne radar data. We exploit this correspondence to derive computationally efficient par...

The main purpose of this work is to contribute the study set-valued random variables by providing a kind Wold decomposition theorem for interval-valued processes. As set not vector space, as established in 1938 Herman applicable them. So, notion pseudovector space introduced and used establish generalization that works covariance stationary time series Before this, autoregressive moving-average...

Let (S1,S2) be a bi-isometry, that is, pair of commuting isometries S1 and S2 on complex Hilbert space H. By the von Neumann-Wold decomposition, hyper-range H∞(S1):=∩n=0∞S1nH reduces to unitary operator. Although H∞(S1) is an invariant subspace for S2, in general, not reducing S2. We show isometry if only subspaces S2(ker⁡S1⁎) H are orthogonal. Further, we describe all bi-isometries satisfying ...

The separation of unobserved sources from mixed observed data is a fundamental signal processing problem. Most proposed techniques for solving this problem rely on independence or at least uncorrelation assumption of source signals. In this paper an algorithm is introduced for source signals that are correlated with each other. The method uses a preprocessing technique based on Wold decompositi...