Through analysing the conditions, it can be known that there were different viewpoints on Gide in the two periods, and it's the result of being effected by double elements, the author's personality and the accepting environment.
A local-global principle is proved by the second named author in the adjacent paper of this volume.
The material presented here is a synopsis of the Ph.D thesis of the author, cf.
Then we also show that the Hilbert series of nonfinitely generated invariant rings appearing in the author's linear counterexamples are rational functions.
In the nontwisted case this description was earlier obtained by the first author.
In this paper we give a further investigation of the method introduced by the author in [1, Frequency-domain bounds for nonnegative unsharply band-limited functions] for proving bounds for functions with nonnegative Fourier transforms.
Recently one of the authors obtained a classification of simple infinite dimensional Lie superalgebras of vector fields which extends the well known classification of E.
The proof of the results uses an extension of the Littlewood-Paley-Stein theory of square functions to the vector-valued case and inequalities previously proved by one of the authors in the context of the Riesz transforms of order one.
The fiberization of affine systems via dual Gramian techniques, which was developed in previous papers of the authors, is applied here for the study of affine frames that have an affine dual system.
Yau's original statement was improved or extended in various directions by a long list of authors.
By taking special values of r, p, s, and u0, these well-posedness results reduce to some of those previously obtained by other authors [4, 14].