The Cayley transform of linear relations
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چکیده
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on the effect of linear & non-linear texts on students comprehension and recalling
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15 صفحه اولThe Cayley Transform of Banach Algebras
A square matrix D is called convergent if limn→∞D = 0, or equivalently, limn→∞‖Dn‖ = 0, where ‖·‖ denotes the matrix norm. A square matrix is called stable if its characteristic values all have negative real parts. The above definitions can be generalized to elements in general complex Banach algebras as follows: let be a complex Banach algebra with norm ‖ · ‖, and let σ(T) be the spectrum of T...
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Given a group G, we can construct a graph relating the elements of G to each other, called the Cayley graph. Using Fourier analysis on a group allows us to apply our knowledge of the group to gain insight into problems about various properties of the graph. Ideas from representation theory are powerful tools for analysis of groups and their Cayley graphs, but we start with some simpler theory t...
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Let G be a simple Lie group of real rank one, with Iwasawa decomposition KAN̄ and Bruhat big cell NMAN̄ . Then the space G/MAN̄ may be (almost) identified with N and with K/M , and these identifications induce the (generalised) Cayley transform C : N → K/M . We show that C is a conformal map of Carnot–Caratheodory manifolds, and that composition with the Cayley transform, combined with multiplicat...
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The uncertainty principle plays an important role in mathematics, physics, signal processing, and so on. Firstly, based on definition of the linear canonical transform (LCT) and the traditional Pitt’s inequality, one novel Pitt’s inequality in the LCT domains is obtained, which is connected with the LCT parameters a and b. Then one novel logarithmic uncertainty principle is derived from this no...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2004
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-04-07551-3