By Mitsuo Morimoto

This ebook treats round harmonic growth of actual analytic services and hyperfunctions at the sphere. simply because a one-dimensional sphere is a circle, the easiest instance of the speculation is that of Fourier sequence of periodic capabilities. the writer first introduces a procedure of advanced neighborhoods of the field by way of the Lie norm. He then experiences holomorphic services and analytic functionals at the advanced sphere. within the one-dimensional case, this corresponds to the learn of holomorphic services and analytic functionals at the annular set within the advanced aircraft, hoping on the Laurent sequence growth. during this quantity, it truly is proven that an analogous thought nonetheless works in a higher-dimensional sphere. The Fourier-Borel transformation of analytic functionals at the sphere is usually tested; the eigenfunction of the Laplacian might be studied during this approach.

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**Example text**

F. F. This yields formalist (considered a new theory 0<~ , 1

We shall say that part 5. Let y : Its source is such that if and only if for each finite y related is to hope that For any r e l a t i o n related by the transfered ~ to all g x of type in F . F 2 , there r e l a t i o n to all elements of the ). The proofs in for the g i v e n enlargement w 5 of and ~ . e. with quantifications only on element -variables). ii) The invocation of F2 Note that we could introduce a type is justified. Fn for n-ary relations, n ~ 2 . But re- grouping the entries, we immediately reduce their number to two.

Also prove that a singular point of First (resp. second) kind is the shadow of a singu/ar of second (resp. First) kind. -analytic surface in whose shadow is the unit square ]R2 . ~R 3 whose shadow is the unit c~be I~3 . 4) Prove that any parabola in in ~2 ~2 is the shadow of some . -hyperbola. -ellipse. whose shadow is a circle Relate these almost symmetries with the symmetries physicists (use the polar equa- * -conics with non standard excentricity 5) Prove that a circle is the shadow of an An * -ellipse of E C .