The parametric Weierstrass integral over a BV curve as a length functional

Loris Faina

Studia Mathematica (1998)

  • Volume: 127, Issue: 1, page 9-19
  • ISSN: 0039-3223

Abstract

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The constructive definition of the Weierstrass integral through only one limit process over finite sums is often preferable to the more sophisticated definition of the Serrin integral, especially for approximation purposes. By proving that the Weierstrass integral over a BV curve is a length functional with respect to a suitable metric, we discover a further natural reason for studying the Weierstrass integral. This characterization was conjectured by Menger.

How to cite

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Faina, Loris. "The parametric Weierstrass integral over a BV curve as a length functional." Studia Mathematica 127.1 (1998): 9-19. <http://eudml.org/doc/216462>.

@article{Faina1998,
abstract = {The constructive definition of the Weierstrass integral through only one limit process over finite sums is often preferable to the more sophisticated definition of the Serrin integral, especially for approximation purposes. By proving that the Weierstrass integral over a BV curve is a length functional with respect to a suitable metric, we discover a further natural reason for studying the Weierstrass integral. This characterization was conjectured by Menger.},
author = {Faina, Loris},
journal = {Studia Mathematica},
keywords = {generalized length; Weierstrass integral over a curve of bounded variation},
language = {eng},
number = {1},
pages = {9-19},
title = {The parametric Weierstrass integral over a BV curve as a length functional},
url = {http://eudml.org/doc/216462},
volume = {127},
year = {1998},
}

TY - JOUR
AU - Faina, Loris
TI - The parametric Weierstrass integral over a BV curve as a length functional
JO - Studia Mathematica
PY - 1998
VL - 127
IS - 1
SP - 9
EP - 19
AB - The constructive definition of the Weierstrass integral through only one limit process over finite sums is often preferable to the more sophisticated definition of the Serrin integral, especially for approximation purposes. By proving that the Weierstrass integral over a BV curve is a length functional with respect to a suitable metric, we discover a further natural reason for studying the Weierstrass integral. This characterization was conjectured by Menger.
LA - eng
KW - generalized length; Weierstrass integral over a curve of bounded variation
UR - http://eudml.org/doc/216462
ER -

References

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