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Full-Text Articles in Algebra
Discrete Wiener Algebra In The Bicomplex Setting, Spectral Factorization With Symmetry, And Superoscillations, Daniel Alpay, Izchak Lewkowicz, Mihaela Vajiac
Discrete Wiener Algebra In The Bicomplex Setting, Spectral Factorization With Symmetry, And Superoscillations, Daniel Alpay, Izchak Lewkowicz, Mihaela Vajiac
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we present parallel theories on constructing Wiener algebras in the bicomplex setting. With the appropriate symmetry condition, the bicomplex matrix valued case can be seen as a complex valued case and, in this matrix valued case, we make the necessary connection between bicomplex analysis and complex analysis with symmetry. We also write an application to superoscillations in this case.
Positivity, Rational Schur Functions, Blaschke Factors, And Other Related Results In The Grassmann Algebra, Daniel Alpay, Ismael L. Paiva, Daniele C. Struppa
Positivity, Rational Schur Functions, Blaschke Factors, And Other Related Results In The Grassmann Algebra, Daniel Alpay, Ismael L. Paiva, Daniele C. Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
We begin a study of Schur analysis in the setting of the Grassmann algebra when the latter is completed with respect to the 1-norm. We focus on the rational case. We start with a theorem on invertibility in the completed algebra, and define a notion of positivity in this setting. We present a series of applications pertaining to Schur analysis, including a counterpart of the Schur algorithm, extension of matrices and rational functions. Other topics considered include Wiener algebra, reproducing kernels Banach modules, and Blaschke factors.
On Algebras Which Are Inductive Limits Of Banach Spaces, Daniel Alpay, Guy Salomon
On Algebras Which Are Inductive Limits Of Banach Spaces, Daniel Alpay, Guy Salomon
Mathematics, Physics, and Computer Science Faculty Articles and Research
We introduce algebras which are inductive limits of Banach spaces and carry inequalities which are counterparts of the inequality for the norm in a Banach algebra. We then define an associated Wiener algebra, and prove the corresponding version of the well-known Wiener theorem. Finally, we consider factorization theory in these algebra, and in particular, in the associated Wiener algebra.