Harmonic Analysis on Totally Disconnected Sets by John Benedetto

By John Benedetto

Publication via Benedetto, John

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Extra resources for Harmonic Analysis on Totally Disconnected Sets

Example text

2 clear is d e n s e Ts6~ Then we with compute corresponding supp v~ from supp T . 1 and ~ = v since in easily C(F) <~,@F > = by Stone , and the - Weierstrass, algebra as generated in Prop. 3. d. 3 Representation Proposition Proof. 5 a. The of First Order Distributions a. ci(r)C_A(r) b. C (F) C. A'(r)C >i(r)Co(r) fact that a continuous , is dense in imbedding. [3]). 3). I 1411 A +tl4'll~ the is Cauchy Cn ÷ ~ result consider ci(r) ÷ has first topology as well con then as pointwise. 9) A ÷ o .

D I ( F ) _ C D ( F ) was a n d k. 3 and S = T CI(F) A ' ( F ) C_ D I ( F ) TEA'(F), it is w e l l - d e f i n e d , by k. d. 6 a. ~ maps Dk(r) function T' onto ^ X b. - {sgDk+I(F) For all : S(O) = O} . TEDk(F) T = c m + S k O w~ere T

D. 5 sense Proof. Note Take Let Let of A'(F) Without that TeA'(F) if , then loss of ¢eA(F), @eA(F), supp and consider ~el ¢eA(F) look and I~ T = 0 [0,2~), on generality supp ¢ C ¢@C_ I all in t h e take I , we and so h>O I open. e. , in of open interval. fact, for all hypothesis. k+h] G I #(y)= i h2 Y - _ 1 h2 k I like _ k-h on l+h 1 y + --~ + h,ye [ ] k,l+h . 11). g. g. d. Corollary Proof. 5. d. Remark for i. every and by ¢, the 2. port ume TeA'(F) supp usual We ; then ¢CU, functional refer T = 0 = 0 .