Derivative of the norm of a linear mapping and its application to differential equations

František Tumajer

Applications of Mathematics (1992)

  • Volume: 37, Issue: 3, page 193-199
  • ISSN: 0862-7940

Abstract

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In this paper the notion of the derivative of the norm of a linear mapping in a normed vector space is introduced. The fundamental properties of the derivative of the norm are established. Using these properties, linear differential equations in a Banach space are studied and lower and upper estimates of the norms of their solutions are derived.

How to cite

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Tumajer, František. "Derivative of the norm of a linear mapping and its application to differential equations." Applications of Mathematics 37.3 (1992): 193-199. <http://eudml.org/doc/15710>.

@article{Tumajer1992,
abstract = {In this paper the notion of the derivative of the norm of a linear mapping in a normed vector space is introduced. The fundamental properties of the derivative of the norm are established. Using these properties, linear differential equations in a Banach space are studied and lower and upper estimates of the norms of their solutions are derived.},
author = {Tumajer, František},
journal = {Applications of Mathematics},
keywords = {derivative of the norm of a linear mapping; linear differential equations in a Banach space; normed space; solution of the differential equation; derivative of the norm of a linear mapping; linear differential equations in a Banach space},
language = {eng},
number = {3},
pages = {193-199},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Derivative of the norm of a linear mapping and its application to differential equations},
url = {http://eudml.org/doc/15710},
volume = {37},
year = {1992},
}

TY - JOUR
AU - Tumajer, František
TI - Derivative of the norm of a linear mapping and its application to differential equations
JO - Applications of Mathematics
PY - 1992
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 37
IS - 3
SP - 193
EP - 199
AB - In this paper the notion of the derivative of the norm of a linear mapping in a normed vector space is introduced. The fundamental properties of the derivative of the norm are established. Using these properties, linear differential equations in a Banach space are studied and lower and upper estimates of the norms of their solutions are derived.
LA - eng
KW - derivative of the norm of a linear mapping; linear differential equations in a Banach space; normed space; solution of the differential equation; derivative of the norm of a linear mapping; linear differential equations in a Banach space
UR - http://eudml.org/doc/15710
ER -

References

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  1. A. N. Kolmogorov S. V. Fomin, Foundations of the theory of functions and functional analysis, (Russian). Czech translation, Praha, 1975. (1975) 
  2. J. Dieudonné, Foundations of modern analysis, Academic Press, New York-London, 1960; Russian translation, Mir, Moscow. (1960) MR0120319

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