"Big" Continuous Restrictions of Arbitrary Functions

被引：5

作者：

Ciesielski, K. C. ^{[1
,2
]}

Martinez-Gomez, M. E. ^{[3
]}

Seoane-Sepulveda, J. B. ^{[4
]}

机构：

[1] West Virginia Univ, Dept Math, Morgantown, WV 26506 USA

[2] Univ Penn, Dept Radiol, MIPG, Philadelphia, PA 19104 USA

[3] Univ Complutense Madrid, Fac Ciencias Matemat, Dept Anal Matemat & Matemat Aplicada, Plaza Ciencias 3, E-28040 Madrid, Spain

[4] Univ Complutense Madrid, Fac Ciencias Matemat, Dept Anal Matemat & Matemat Aplicada, IMI, Plaza Ciencias 3, E-28040 Madrid, Spain

来源：

AMERICAN MATHEMATICAL MONTHLY | 2019年 / 126卷 / 06期

关键词：

D O I：

10.1080/00029890.2019.1586263

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We discuss an amazing 1922 result of Henry Blumberg that for an arbitrary , there is a dense such that the restriction is continuous. In particular, we provide a new short proof of this theorem.

引用

页码：547 / 552

页数：6

共 50 条

[31] Continuous restrictions of linear operators
Shkarin, SA
[J]. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2001, 4 (01) : 121 - 136
[32] Univalent functions with range restrictions
Kirsch, S
[J]. ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2000, 19 (04): : 1057 - 1073
[33] RESTRICTIONS OF HP FUNCTIONS IN THE POLYDISK
CLARK, DN
[J]. AMERICAN JOURNAL OF MATHEMATICS, 1988, 110 (06) : 1119 - 1152
[34] On the number of step functions with restrictions
Ahlswede, R.
Blinovsky, V.
[J]. THEORY OF PROBABILITY AND ITS APPLICATIONS, 2006, 50 (04) : 537 - 560
[35] RESTRICTIONS OF ANALYTIC-FUNCTIONS
ROSENBLUM, M
ROVNYAK, J
[J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 22 (01): : A124 - A125
[36] DIFFERENTIABLE RESTRICTIONS OF REAL FUNCTIONS
BROWN, JB
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 108 (02) : 391 - 398
[37] Correlation Analysis of the PLL with an Arbitrary Filter Based on Continuous Piecewise-Linear Functions
Surzhik, D. I.
Vasilyev, G. S.
[J]. 2013 INTERNATIONAL SIBERIAN CONFERENCE ON CONTROL AND COMMUNICATIONS (SIBCON), 2013,
[38] The construction of a Pfaff system with arbitrary piecewise continuous characteristic power-law functions
Izobov, NA
Krupchik, EN
[J]. DIFFERENTIAL EQUATIONS, 2005, 41 (02) : 184 - 194
[39] The Construction of a Pfaff System with Arbitrary Piecewise Continuous Characteristic Power-Law Functions
N. A. Izobov
E. N. Krupchik
[J]. Differential Equations, 2005, 41 : 184 - 194
[40] THE METHOD OF ARBITRARY FUNCTIONS
PLATO, JV
[J]. BRITISH JOURNAL FOR THE PHILOSOPHY OF SCIENCE, 1983, 34 (01): : 37 - 47

← 1 2 3 4 5 →