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Uniform Norm: Mathematical Analysis, Norm, Real Number, Complex Number, Supremum, Metric, Continuous Function, Interval - Softcover
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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.
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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.
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Uniform Norm
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VDM Verlag Dr. Müller E.K. Feb 2010, 2010
ISBN 10: 6130353723
ISBN 13: 9786130353728
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -High Quality Content by WIKIPEDIA articles! 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. Englisch. Seller Inventory # 9786130353728
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Uniform Norm : Mathematical Analysis, Norm, Real Number, Complex Number, Supremum, Metric, Continuous Function, Interval
Published by
VDM Verlag Dr. Müller E.K., 2010
ISBN 10: 6130353723
ISBN 13: 9786130353728
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Taschenbuch
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Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! 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. Seller Inventory # 9786130353728
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Uniform Norm | Mathematical Analysis, Norm, Real Number, Complex Number, Supremum, Metric, Continuous Function, Interval
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Taschenbuch. Condition: Neu. Uniform Norm | Mathematical Analysis, Norm, Real Number, Complex Number, Supremum, Metric, Continuous Function, Interval | Lambert M. Surhone (u. a.) | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786130353728 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu Print on Demand. Seller Inventory # 101343256