## Analytic Functionals Near R[superscript N] |

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9 e G 9 in G absolutely convergent analytic functional analytic kernel APPENDIX associated Hermite series bounded canonical representation Cauchy CHAPTER compact support complex analysis Consequently consider contour compatible converge in G converges absolutely converges uniformly coordinate patch David Stanton Rosenthal define dissertation DISTRIBUTIONS OF COMPACT Doctor Frank Doctor of Philosophy estimate exists fact that G fi(z finite fiv(z fl(z flv(z Fourier transform functionals in G G and G G is dense growth hence Hermite functions Hermitian series holomorphic inequality integral ix-h kernel compatible LEMMA linear log M(z maximum Moreover Mp(z multi-index n-dimensional normed space nuclear space numbers p-strip polynomial Proof properties prove q-norm Riemann sum San Diego Schwartz space sequence single-valued space G strip functions subspaces suitable support contained surface test space THEOREM Thiess uniform convergence z)dz