Banachi ruum

olemus
normeeritud ruum, mis
normi abil defineeritud kauguse
$$d(x,y) = ||x - y||$$ mõttes
on täielik meetriline ruum
=
a complete normed vector space in mathematical analysis

näiteid
= $$n$$-mõõtmeline
Eukleidiline vektorruum $$\mathbb{R}^n$$, milles
vektori $$x=(x_1,x_2,\ldots,x_n)$$ norm
on $$||x||_p = \sqrt[p]{|x_1|^p + |x_2|^p + \ldots + |x_n|^p}$$

= seost $$\sum_i |x_i|^p<\infty$$ rahuldavate
reaalarvujadade $$x=(x_0,x_1, x_2, \ldots )$$
vektorruum normiga $$||x||_p = \sqrt[p]{\sum_i |xi|^p}$$

ülevaateid
https://www.techopedia.com/definition/17852/banach-space

https://en.wikipedia.org/wiki/Banach_space

https://encyclopediaofmath.org/wiki/Banach_space

http://www.math.ncku.edu.tw/~rchen/2015%20Teaching/Metric%20Space_Notes%20%28Georgia%20Tech%29.pdf

https://www.math.ucdavis.edu/~hunter/book/ch5.pdf

http://www.ma.huji.ac.il/~razk/iWeb/My_Site/Teaching_files/Banach.pdf

Banachi ruum

olemus
normeeritud ruum, mis
normi abil defineeritud kauguse
$$d(x,y) = ||x - y||$$ mõttes
on täielik meetriline ruum
=
a complete normed vector space in mathematical analysis

näiteid
= $$n$$-mõõtmeline
Eukleidiline vektorruum $$\mathbb{R}^n$$, milles
vektori $$x=(x_1,x_2,\ldots,x_n)$$ norm
on $$||x||_p = \sqrt[p]{|x_1|^p + |x_2|^p + \ldots + |x_n|^p}$$

= seost $$\sum_i |x_i|^p<\infty$$ rahuldavate
reaalarvujadade $$x=(x_0,x_1, x_2, \ldots )$$
vektorruum normiga $$||x||_p = \sqrt[p]{\sum_i |xi|^p}$$

ülevaateid
https://www.techopedia.com/definition/17852/banach-space

https://en.wikipedia.org/wiki/Banach_space

https://encyclopediaofmath.org/wiki/Banach_space

http://www.math.ncku.edu.tw/~rchen/2015%20Teaching/Metric%20Space_Notes%20%28Georgia%20Tech%29.pdf

https://www.math.ucdavis.edu/~hunter/book/ch5.pdf

http://www.ma.huji.ac.il/~razk/iWeb/My_Site/Teaching_files/Banach.pdf

Palun oodake...

Banachi ruum

olemus
normeeritud ruum, mis
normi abil defineeritud kauguse
$$d(x,y) = ||x - y||$$ mõttes
on täielik meetriline ruum
=
a complete normed vector space in mathematical analysis

näiteid
= $$n$$-mõõtmeline
Eukleidiline vektorruum $$\mathbb{R}^n$$, milles
vektori $$x=(x_1,x_2,\ldots,x_n)$$ norm
on $$||x||_p = \sqrt[p]{|x_1|^p + |x_2|^p + \ldots + |x_n|^p}$$

= seost $$\sum_i |x_i|^p<\infty$$ rahuldavate
reaalarvujadade $$x=(x_0,x_1, x_2, \ldots )$$
vektorruum normiga $$||x||_p = \sqrt[p]{\sum_i |xi|^p}$$

ülevaateid
https://www.techopedia.com/definition/17852/banach-space

https://en.wikipedia.org/wiki/Banach_space

https://encyclopediaofmath.org/wiki/Banach_space

http://www.math.ncku.edu.tw/~rchen/2015%20Teaching/Metric%20Space_Notes%20%28Georgia%20Tech%29.pdf

https://www.math.ucdavis.edu/~hunter/book/ch5.pdf

http://www.ma.huji.ac.il/~razk/iWeb/My_Site/Teaching_files/Banach.pdf

Andmete allalaadimisel või töötlemisel esines tehniline tõrge.
Vabandame!