In
mathematics, two
real number
In mathematics, a real number is a number that can be used to measurement, measure a ''continuous'' one-dimensional quantity such as a distance, time, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small var ...
s
are called conjugate indices (or Hölder conjugates) if
:
Formally, we also define
as conjugate to
and
vice versa
References
Additional references
*
*
{{Latin phrases
V
ca:Locució llatina#V
da:Latinske ord og vendinger#V
fr:Liste de locutions latines#V
id:Daftar frasa Latin#V
it:Locuzioni latine#V
nl:Lijst van Latijnse spreekwoorden en ui ...
.
Conjugate indices are used in
Hölder's inequality
In mathematical analysis, Hölder's inequality, named after Otto Hölder, is a fundamental inequality between integrals and an indispensable tool for the study of spaces.
:Theorem (Hölder's inequality). Let be a measure space and let with . ...
. If
are conjugate indices, the spaces ''L''
''p'' and ''L''
''q'' are
dual
Dual or Duals may refer to:
Paired/two things
* Dual (mathematics), a notion of paired concepts that mirror one another
** Dual (category theory), a formalization of mathematical duality
*** see more cases in :Duality theories
* Dual (grammatical ...
to each other (see
''L''''p'' space).
See also
*
Beatty's theorem
In mathematics, a Beatty sequence (or homogeneous Beatty sequence) is the sequence of integers found by taking the floor of the positive multiples of a positive irrational number. Beatty sequences are named after Samuel Beatty, who wrote about t ...
References
* Antonevich, A. ''Linear Functional Equations'', Birkhäuser, 1999. .
Functional analysis
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