关于连续细分方程的一个注记_英文_

关于连续细分方程的一个注记_英文_ () A r t icl 23085 20000220048205 : 1005ID A N o te on Con t inuou s R ef inem en t α E qua t ion s L i Yunzhang (). . . , 100022D ep a r tof A pp lM a thB eijing Po ly tech n ic U n iver sityB eijing D a i X in rong (), 310000 . . Zh ejiang Po ly tech n ic U n iver sityH angzhou PRC h ina A b st ract In th is p ap e r som e cr ite r ia of th e ex istence of th e so lu t ion s to con t inuou s ref inem en t equa t ion s in p s () () L R 1 Φ p Φ ? a re ob ta ined , Keyw o rd s R ef inem en t E qua t ionCon t inuou s R ef inem en t E qua t ion () 19914215 CL C n um ber: O 174. 2 D ocum en t code: A C la ssif ica t ion AM S C 1 In t roduct ion s () s lZ , L et be a f ixed po sit ive in teger0 deno te th e linea r sp ace of a ll f in itely suppo r ted s Z . , sequences on In th is p ap erw e invest iga te th e con t inuou s ref inem en t equa t ion s of th e fo rm () ( ) () ()f r= a tf M r-1 tt d s ?R s? s) () (f , a L R, Rrw h ere is th e unk now n funct ion on is a com p act ly suppo r ted funct ion in and -n M is an s × s d ila t ion m a t r ix th a t m ean s M is an s × s in teger m a t r ix such th a t lim M =0 .n?? () 1T h e equa t ion is a coun terp a r t of th e fo llow ing ref inem en t equa t ion () () ()()f = a k f M - k 2 rr? s k?Zs s( ) w h ere f is th e unk now n funct ion on R , a ? l0 Z , and M is an s × s d ila t ion m a t r ix. ( ) 2T h e ref inem en t equa t ion s of th e fo rm p lay an im po r tan t ro le in w avelet ana ly sis and , , , . , com p u ter g rap h icsandso fa rr ich f ru it s fo r w h ich h ave been ob ta inedIn recen t yea r sth e ( ) s = 1 M = 2 , 1. equa t ion s of th e fo rm w ere add ressed by som e m th em a t ician sW h en and ( )1 4 , 2 p robab ility app roach w a s develop ed to study in and f requencydom a in app roach w a s () () () 13 . s = 1,M = 2, a r= ς r, u sed to study in W h en and - 1, 1 it s so lu t ion is k now n a s22. , th e up funct ionT h e up funct ion h a s in terest ing p rop er t ies and im po r tan t app lica t ion sand h a s )( 8 , 11 . been ex ten sively stud ied by m any m a th em a t ician s see n n a a 1 Φ p Φ ?. {S }T }{ G iven W e def ine th e op era to r sequences n?N and n?N by () () ( ) S g r= a r- tg td t,a M s ?R n+ 1 n () () () g g S a r= S a S a r, () ( ) ( ) T g r= a tg r- td t,a M s ?R n+ 1 n () () () T a g r= T a T a g r 1 s () g ? L R fo r P u t t ing s ) (() | Φ 1 1 - , x i||x = x , x s ,, | x ifo r 1 () () 0 , th ere ex ist s N ? N such th a t - n () () ? f r- M t- f r? p <Ε s n >t ? -1, 1 N . and fo r ,H ence - n () ) ( ) (lim ? f r- M t- f 数学

数学高考答题卡模板高考数学答题卡模板三年级数学混合运算测试卷数学作业设计案例新人教版八年级上数学教学计划