Schwartz DistributionsDepartment of Pure Mathematics, School of General Studies; Department of Mathematics, Institute of Advanced Studies, Australian National University, 1969 - Mathematics - 95 pages |
Common terms and phrases
absolutely integrable arbitrary bounded support Co-function constant distribution containing the support continuous functions convolution of distributions convolution of functions Corollary corresponding differentiable functions distribution derivative distribution of bounded distributions of slow elementary solution equation equivalence classes example fact finite number finite order follows Fourier coefficients Fourier series Fourier transforms functions f functions of slow given hence hypoelliptic implies infinitely interval a,b k₁ k₂ linear functional locally integrable functions m₁ mapping notation Note null set open interval open interval containing periodic distribution periodic functions polynomial function primitives Proof properties prove Pure Mathematics remark Schwartz's distributions slow growth space of distributions subspace tends to zero test functions Theorem trigonometric series uniformly vector space Εμ εν Σα φε φεν φες ΦΤ ψε