Uniform Norm: Mathematical Analysis, Norm, Real Number, Complex Number, Supremum, Metric, Continuous Function, Interval - Couverture souple

 
9786130353728: Uniform Norm: Mathematical Analysis, Norm, Real Number, Complex Number, Supremum, Metric, Continuous Function, Interval
Couverture souple
ISBN 10 : 6130353723 ISBN 13 : 9786130353728
Editeur : Betascript Publishing, 2010

Synopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. n mathematical analysis, the uniform norm assigns to real- or complex-valued bounded functions f defined on a set S the nonnegative number |f|_infty=|f|_{infty,S}=supleft{,left|f(x)right|:xin S,right}. This norm is also called the supremum norm, the Chebyshev norm, or the infinity norm. If we allow unbounded functions, this formula does not yield a norm or metric in a strict sense, although the obtained so-called extended metric still allows one to define a topology on the function space in question. If f is a continuous function on a closed interval, or more generally a compact set, then it is bounded and the supremum in the above definition is attained by the Weierstrass extreme value theorem, so we can replace the supremum by the maximum. In this case, the norm is also called the maximum norm.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. n mathematical analysis, the uniform norm assigns to real- or complex-valued bounded functions f defined on a set S the nonnegative number |f|_infty=|f|_{infty,S}=supleft{,left|f(x)right|:xin S,right}. This norm is also called the supremum norm, the Chebyshev norm, or the infinity norm. If we allow unbounded functions, this formula does not yield a norm or metric in a strict sense, although the obtained so-called extended metric still allows one to define a topology on the function space in question. If f is a continuous function on a closed interval, or more generally a compact set, then it is bounded and the supremum in the above definition is attained by the Weierstrass extreme value theorem, so we can replace the supremum by the maximum. In this case, the norm is also called the maximum norm.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Betascript Publishing
Date d'édition
2010
Langue
anglais
ISBN 10 
6130353723
ISBN 13 
9786130353728
Reliure
Broché
Nombre de pages
76
Éditeur
Surhone Lambert M., Tennoe Mariam T., Henssonow Susan F.
Coordonnées du fabricant
non disponible
Personne responsable
non disponible