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Explore Parseval through 7 example sentences from English. Ideal for language learners, writers and word enthusiasts.

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Parseval in a sentence

Context around Parseval

  • Average sentence length in these examples: 23 words
  • Position in the sentence: 1 start, 5 middle, 1 end
  • Sentence types: 7 statements, 0 questions, 0 exclamations

Often before:

valued 1× plancherel 1× instance 1× summands 1×

Often after:

periodicity 1×

Sentence patterns with Parseval

These short patterns come directly from the example sentences and show how the word is often embedded:

banach valued parseval s theorem 1× for instance parseval s identity 1× many summands parseval s identity 1× of the parseval s theorem 1× orthogonality plancherel parseval periodicity shift 1× parseval s theorem 1× s and parseval s theorem 1×

Sentence openings and endings

Common sentence openings:

in the same 1× parseval s theorem 1× plancherel theorem is 1× such properties include 1× this allows us 1×

Common sentence endings:

an infinite sum 1× inner product space 1× many fft algorithms 1× parseval s theorem 1× proved by liapounoff 1× to hilbert spaces 1×

Words around Parseval

Just before it in the word index:

parses 16 parsers 46 parser 112 parseltongue 5 parsells 2 parsell 3

Just after it in the word index:

parsey 2 parsha 5 parshall 7 parshottam 5 parshuram 4 parshurama 2

Similar in corpus frequency:

aaba 10 aafc 10 aaib 10 aalbers 10 abbate 10 abbesses 10

Corpus analysis for Parseval

  • In this selection, "parseval" usually appears in the middle of the sentence. The average example has 23 words, and this corpus slice is mostly made up of statements.
  • Around the word, valued, plancherel, instance and periodicity stand out and add context to how "parseval" is used.
  • Recognizable usage signals include banach valued parseval s theorem and for instance parseval s identity. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "parseval" sits close to words such as aaba, aafc and aaib, which helps place it inside the broader word index.

Example types with parseval

The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:

Short example sentences

Parseval's theorem was proved only for Fourier series, and was first proved by Liapounoff. (15 words)

Such properties include the completeness, orthogonality, Plancherel/Parseval, periodicity, shift, convolution, and unitarity properties above, as well as many FFT algorithms. (21 words)

All of the basic properties listed above hold for the n-dimensional Fourier transform, as do Plancherel's and Parseval's theorem. (22 words)

Longer example sentences

There are also many less common ways of calculating definite integrals; for instance, Parseval's identity can be used to transform an integral over a rectangular region into an infinite sum. (31 words)

In the same article, Kwapień proved that the validity of a Banach-valued Parseval's theorem for the Fourier transform characterizes Banach spaces isomorphic to Hilbert spaces. (27 words)

Plancherel theorem is a special case of the Parseval's theorem and states: : These theorems are also equivalent to the unitary condition below. (23 words)

Example sentences (7)

All of the basic properties listed above hold for the n-dimensional Fourier transform, as do Plancherel's and Parseval's theorem.

In the same article, Kwapień proved that the validity of a Banach-valued Parseval's theorem for the Fourier transform characterizes Banach spaces isomorphic to Hilbert spaces.

Parseval's theorem was proved only for Fourier series, and was first proved by Liapounoff.

Plancherel theorem is a special case of the Parseval's theorem and states: : These theorems are also equivalent to the unitary condition below.

Such properties include the completeness, orthogonality, Plancherel/Parseval, periodicity, shift, convolution, and unitarity properties above, as well as many FFT algorithms.

There are also many less common ways of calculating definite integrals; for instance, Parseval's identity can be used to transform an integral over a rectangular region into an infinite sum.

This allows us to extend Pythagoras' theorem to infinitely many summands: *Parseval's identity: Suppose V is a complete inner product space.

Frequently asked questions

How do you use "parseval" in a sentence?
An example: "All of the basic properties listed above hold for the n-dimensional Fourier transform, as do Plancherel's and Parseval's theorem." This page contains 7 example sentences with the word "parseval" from authentic English texts.
How many example sentences with "parseval" are there?
Voorbeeldzinnen.info contains 7 example sentences with "parseval", drawn from a database of millions of English sentences.