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Articles 1 - 6 of 6
Full-Text Articles in Algebra
Q-Rational Functions And Interpolation With Complete Nevanlinna–Pick Kernels, Daniel Alpay, Paula Cerejeiras, Uwe Kaehler, Baruch Schneider
Q-Rational Functions And Interpolation With Complete Nevanlinna–Pick Kernels, Daniel Alpay, Paula Cerejeiras, Uwe Kaehler, Baruch Schneider
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we introduce the concept of matrix-valued q-rational functions. In comparison to the classical case, we give different characterizations with principal emphasis on realizations and discuss algebraic manipulations. We also study the concept of Schur multipliers and complete Nevanlinna–Pick kernels in the context of q-deformed reproducing kernel Hilbert spaces and provide first applications in terms of an interpolation problem using Schur multipliers and complete Nevanlinna–Pick kernels.
S-Preclones And The Galois Connection SPol–SInv, Part I, Peter Jipsen, Erkko Lehtonen, Reinhard Pöschel
S-Preclones And The Galois Connection SPol–SInv, Part I, Peter Jipsen, Erkko Lehtonen, Reinhard Pöschel
Mathematics, Physics, and Computer Science Faculty Articles and Research
We consider S-operations f : An → A in which each argument is assigned a signum s ∈ S representing a “property” such as being order- preserving or order-reversing with respect to a fixed partial order on A. The set S of such properties is assumed to have a monoid structure reflecting the behaviour of these properties under the composition of S-operations (e.g., order-reversing composed with order-reversing is order- preserving). The collection of all S-operations with prescribed properties for their signed arguments is not a clone (since it is not closed under arbitrary identification of arguments), …
Schur Analysis Over The Unit Spectral Ball, Daniel Alpay, Ilwoo Choo
Schur Analysis Over The Unit Spectral Ball, Daniel Alpay, Ilwoo Choo
Mathematics, Physics, and Computer Science Faculty Articles and Research
We begin a study of Schur analysis when the variable is now a matrix rather than a complex number. We define the corresponding Hardy space, Schur multipliers and their realizations, and interpolation. Possible applications of the present work include matrices of quaternions, matrices of split quaternions, and other algebras of hypercomplex numbers.
Regular Functions On The Scaled Hypercomplex Numbers, Daniel Alpay, Ilwoo Cho
Regular Functions On The Scaled Hypercomplex Numbers, Daniel Alpay, Ilwoo Cho
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper, we study the regularity of R-differentiable functions on open connected subsets of the scaled hypercomplex numbers {Ht}t∈R by studying the kernels of suitable differential operators {∇t}t∈R, up to scales in the real field R.
Spacetime Geometry Of Acoustics And Electromagnetism, Lucas Burns, Tatsuya Daniel, Stephon Alexander, Justin Dressel
Spacetime Geometry Of Acoustics And Electromagnetism, Lucas Burns, Tatsuya Daniel, Stephon Alexander, Justin Dressel
Mathematics, Physics, and Computer Science Faculty Articles and Research
Both acoustics and electromagnetism represent measurable fields in terms of dynamical potential fields. Electromagnetic force-fields form a spacetime bivector that is represented by a dynamical energy–momentum 4-vector potential field. Acoustic pressure and velocity fields form an energy–momentum density 4-vector field that is represented by a dynamical action scalar potential field. Surprisingly, standard field theory analyses of spin angular momentum based on these traditional potential representations contradict recent experiments, which motivates a careful reassessment of both theories. We analyze extensions of both theories that use the full geometric structure of spacetime to respect essential symmetries enforced by vacuum wave propagation. The …
A Little More On Ideals Associated With Sublocales, Oghenetega Ighedo, Grace Wakesho Kivunga, Dorca Nyamusi Stephen
A Little More On Ideals Associated With Sublocales, Oghenetega Ighedo, Grace Wakesho Kivunga, Dorca Nyamusi Stephen
Mathematics, Physics, and Computer Science Faculty Articles and Research
As usual, let RL denote the ring of real-valued continuous functions on a completely regular frame L. Let βL and λL denote the Stone- Čech compactification of L and the Lindelöf coreflection of L, respectively. There is a natural way of associating with each sublocale of βL two ideals of RL, motivated by a similar situation in C(X). In [12], the authors go one step further and associate with each sublocale of λL an ideal of RL in a manner similar to one of the ways one does it for sublocales of βL. The intent in this paper …