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

 
9786130353728: Uniform Norm: Mathematical Analysis, Norm, Real Number, Complex Number, Supremum, Metric, Continuous Function, Interval
Softcover
ISBN 10: 6130353723 ISBN 13: 9786130353728
Verlag: Betascript Publishers, 2010

Inhaltsangabe

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.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Reseña del editor

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.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Betascript Publishers
Erscheinungsdatum
2010
Sprache
Englisch
ISBN 10 
6130353723
ISBN 13 
9786130353728
Einband
Tapa blanda
Anzahl der Seiten
76
Herausgeber
Surhone Lambert M., Tennoe Mariam T., Henssonow Susan F.
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
Nicht verfügbar