article · 2003

On the Effective Jordan Decomposability

Xiangfeng Zheng, Robert Rettinger, Burchard von Braunmühl

Cited by 0Abstract and details only

Abstract

The classical Jordan decomposition Theorem says that any real function of bounded variation can be expressed as a difference of two increasing functions. This paper explores the effective version of Jordan decomposition. We give a sufficient and necessary condition for those computable real functions of bounded variation which can be expressed as a difference of two computable increasing functions. Using this condition, we prove further that there is a computable real function which has even a computable modulus of absolute continuity (hence is of bounded variation) but it is not a difference of any two computable increasing functions. The polynomial time version of this result holds too and this gives a negative answer to an open question of Ko in [6].

Cite this paper

APA 7

Zheng, X., Rettinger, R., & von Braunmühl, B. (2003). On the Effective Jordan Decomposability.

MLA 9

Zheng, Xiangfeng, et al. “On the Effective Jordan Decomposability.” 2003.

Chicago

Zheng, Xiangfeng, Robert Rettinger, and Burchard von Braunmühl. 2003. “On the Effective Jordan Decomposability.”

Harvard

Zheng, X., Rettinger, R. and von Braunmühl, B. (2003) ‘On the Effective Jordan Decomposability’.

BibTeX

@article{zheng2003effective,
  title = {{On the Effective Jordan Decomposability}},
  author = {Zheng, Xiangfeng and Rettinger, Robert and von Braunmühl, Burchard},
  year = {2003}
}

Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.