Beauty and the Beast

We show that a discrete fixed point theorem of Eilenberg is equivalent to the restriction of the contraction principle to the class of non-Archimedean bounded metric spaces.. We

Instead an elementary random occurrence will be denoted by the variable (though unpredictable) element x of the (now Cartesian) sample space, and a general random variable will

We have formulated and discussed our main results for scalar equations where the solutions remain of a single sign. This restriction has enabled us to achieve sharp results on

8.1 In § 8.1 ∼ § 8.3, we give some explicit formulas on the Jacobi functions, which are key to the proof of the Parseval-Plancherel type formula of branching laws of

So far, most spectral and analytic properties mirror of M Z 0 those of periodic Schr¨odinger operators, but there are two important differences: (i) M 0 is not bounded from below

In addition, under the above assumptions, we show, as in the uniform norm, that a function in L 1 (K, ν) has a strongly unique best approximant if and only if the best

The explicit treatment of the metaplectic representa- tion requires various methods from analysis and geometry, in addition to the algebraic methods; and it is our aim in a series

We have avoided most of the references to the theory of semisimple Lie groups and representation theory, and instead given direct constructions of the key objects, such as for