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Full-Text Articles in Algebra
On Free Stochastic Processes And Their Derivatives, Daniel Alpay, Palle Jorgensen, Guy Salomon
On Free Stochastic Processes And Their Derivatives, Daniel Alpay, Palle Jorgensen, Guy Salomon
Mathematics, Physics, and Computer Science Faculty Articles and Research
We study a family of free stochastic processes whose covariance kernels K may be derived as a transform of a tempered measure σ. These processes arise, for example, in consideration non-commutative analysis involving free probability. Hence our use of semi-circle distributions, as opposed to Gaussians. In this setting we find an orthonormal bases in the corresponding noncommutative L2 of sample-space. We define a stochastic integral for our family of free processes.
Non-Commutative Stochastic Distributions And Applications To Linear Systems Theory, Daniel Alpay, Guy Salomon
Non-Commutative Stochastic Distributions And Applications To Linear Systems Theory, Daniel Alpay, Guy Salomon
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper, we introduce a non-commutative space of stochastic distributions, which contains the non-commutative white noise space, and forms, together with a natural multiplication, a topological algebra. Special inequalities which hold in this space allow to characterize its invertible elements and to develop an appropriate framework of non-commutative stochastic linear systems.
Topological Convolution Algebras, Daniel Alpay, Guy Salomon
Topological Convolution Algebras, Daniel Alpay, Guy Salomon
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we introduce a new family of topological convolution algebras of the form ⋃p∈NL2(S,μp), where S is a Borel semi-group in a locally compact group G, which carries an inequality of the type ∥f∗g∥p≤Ap,q∥f∥q∥g∥p for p>q+d where d pre-assigned, and Ap,q is a constant. We give a sufficient condition on the measures μp for such an inequality to hold. We study the functional calculus and the spectrum of the elements of these algebras, and present two examples, one in the setting of non commutative stochastic distributions, and the other related to Dirichlet series.