In this work we introduce a theory of stochastic integration for operator-valued integrands with respect to some classes cylindrical martingale-valued measures in Hilbert spaces. The integral is constructed via the radonification martingales by Hilbert-Schmidt operator theorem and unifies several other theories particular, our covers space valued L\'{e}vy process (which not required satisfy any...

In 1,2 or 3 dimensions a scalar wave excited by a non-negative source in a viscoelastic medium with a non-negative relaxation spectrum or a Newtonian response or both combined inherits the sign of the source. The key assumption is a constitutive relation which involves the sum of a Newtonian viscosity term and a memory term with a completely monotone relaxation kernel. In higher-dimensional spa...

An explicit construction characterizing the operator-valued Bergman inner functions is given for a class of vector-valued standard weighted Bergman spaces in the unit disk. These operator-valued Bergman inner functions act as contractive multipliers from the Hardy space into the associated Bergman space, and they have a natural interpretation as transfer functions for a related class of discret...

In this paper we will prove the equivalence between L-valued logics and L-indexed families of bivaluated logics. It is also proved that this equivalence can be used as a tool for checking compactness and decidability properties of a L-valued logic.

and Applied Analysis 3 3. Main Results Throughout this paper, we will consider lattices as complete lattices,X will denote space, and μ is a membership function of any fuzzy set X. Definition 3.1. If m : σ L → R ∪ {∞} satisfies the following properties, then m is called a lattice measure on the lattice σ-algebra σ L . i m ∅ L0. ii For all f, g ∈ σ L such that m f , m g ≥ L0 : f ≤ g ⇒ m f ≤ m g ...

In the literature, the bounds of the peak to average power ratio (PAPR) are generalized to both complex-valued and real-valued orthogonal frequency division multiplexing (OFDM) signals. In fact, these bounds are accurately bounding the PAPR distribution of complex-valued OFDM signals only. In this paper, we derive accurate PAPR bounds of real-valued OFDM signals and show that bounds of complex-...