gair-sthaaniya prachaalak

ganit mein, ack gair-sthaaniya prachaalak ack maanchitran haye joe ack sthalaakritik sthaan parr karyon koo iss tarah seey mapp kartaa haye kii kissy diye gaye bindu parr output function kaa moolya kissy bhee bindu key kissy bhee pados mein input function key moolyon seey poori tarah seey nirdhaarit naheen kiya jaa sakata haye. gair-sthaaniya prachaalak kaa ack udaaharan forier parivartan haye.
aupchaarik paribhasha.
maan leejiye kii sootra _ 1 ack topological space haye, sootra _ 2 ack sett haye, sootra _ 3 ack function space haye jisamen domen sootra _ 1 key saath function hain, aur sootra _ 5 ack function space haye jisamen domen sootra _ 2 key saath function hain. sootra _ 3 mein dou function sootra _ 7 aur sootra _ 8 koo sootra _ 10 parr samkaksh kahaa jaataa haye yadi sootra _ 12 kaa ack pados sootra _ 11 maujood haye tou sootra _ 14 kaa sootra _ 13 aisaa haye kii ack operator sootra _ 15 koo sthaaniya kahaa jaataa haye yadi pratyek sootra _ 16 key liye ack sootra _ 10 maujood haye tou sabhi karyon key liye sootra _ 7 aur sootra _ 8 sootra _ 3 mein joe sootra _ 12 mein samkaksh hain. ack gair-sthaaniya operator ack operator haye joe sthaaniya naheen haye.
ack sthaaniya prachaalak key liye yeh (siddhant mein) sambhav haye kii vaha ack bindu sootra _ 12 key manmaane dhang seey chhote pados mein sootra _ 7 key moolyon key kewal gyaan kaa upayog karke moolya sootra _ 23 kii ganana karey. ack gair-sthaaniya prachaalak key liye yeh sambhav naheen haye.
udaaharan.
antar prachaalak sthaaniya prachaalak key udaaharan hain. (raikhik) gair-sthaaniya prachaalak kaa ack badaa varg samakalan parivartanon dwara diyaa jaataa haye, jaise kii fourier parivartan aur lapless parivartan. roop key ack abhinn parivartan key liye
jahan sootra _ 27 kuchh kernell function haye, sootra _ 31 parr sootra _ 30 key moolya kii ganana karane key liye sootra _ 29 key samarthan parr lagbhag harr jagah sootra _ 7 key moolyon koo jaanana aavashyak haye.
ekvachan samakalan prachaalak kaa ack udaaharan anshgat laplacian haye.
anuprayog.
gair-sthaaniya prachaalak key anuprayogon key kuchh udaaharan hainh

