M a o i i Univei'si:~; F2ii'f&v, ?' A 22030 .-.,~n e >he*! F !J! quaternionic hpeifiin;:i;?n< is introduced as the sheaf of boundary lralues el qualernionic regular iunctii;ns. A Kothe duality type theorem 1s evtahiiched to prove the isomorphism between compactiy supported quaiernionic Iiyperfunciions and cornpab!~ suppcrted regukr iuncrionals. Ordinary dlfieren!ial operators are studied on the sheaf F with the .uc of the C -K product. Fina!!y 2 sheaf of quaternionic microfunctions is introduced as the microlocalization of 3, and its main properties are studied.
We give an alternative representation of the closure of the Bochner transform of a holomorphic almost periodic mapping in a tube domain. For such mappings we introduce a new notion of amoeba and we show that, for mappings which are regular in the sense of Ronkin, this new notion agrees with Favorov's one. We prove that the amoeba complement of a regular holomorphic almost periodic mapping, defined on C n and taking its values in C m+1 , is a Henriques m-convex subset of R n . Finally, we compare some different notions of regularity.
Abstract. We provide explicit bounds for the degrees of the polynomials which appear as the entries of the left inverse of a polynomial matrix F. When such an inverse does not exist, bounds can be given for the entries of the (1)-inverse of F.
A combinatorial criterium for detecting the normality of the semigroup under the toric deformation (initial algebra of the coordinate ring) of the Hankel projective variety is studied and applied. We discuss properties of the affine semigroup.
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