Some remarks on functions of -bounded variation

Authors:
S. Perlman and D. Waterman

Journal:
Proc. Amer. Math. Soc. **74** (1979), 113-118

MSC:
Primary 26A45

DOI:
https://doi.org/10.1090/S0002-9939-1979-0521883-X

MathSciNet review:
521883

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that if a function has no external saltus, then its total -variation is independent of its values at points of discontinuity, and a function which is equal to the given function at points of continuity cannot have a lesser total -variation. Necessary and sufficient conditions are determined for one space to contain another and for two spaces to be identical.

**[1]**A. Baernstein and D. Waterman,*Functions whose Fourier series converge uniformly for every change of variable*, Indiana Univ. Math. J.**22**(1972), 569-576. MR**0310523 (46:9621)****[2]**C. Goffman,*Everywhere convergence of Fourier series*, Indiana Univ. Math. J.**20**(1970), 107-113. MR**0270048 (42:4941)****[3]**C. Goffman and D. Waterman,*Functions whose Fourier series converge for every change of variable*, Proc. Amer. Math. Soc.**19**(1968), 80-86. MR**0221193 (36:4245)****[4]**-,*A characterization of the class of functions whose Fourier series converge for every change of variable*, J. London Math. Soc. (2)**10**(1975), 69-74. MR**0370036 (51:6265)****[5]**-,*The localization principle for double Fourier series*(to appear).**[6]**S. Perlman,*Functions of generalized variation*, Fund. Math. (to appear). MR**580582 (81h:26007)****[7]**D. Waterman,*On convergence of Fourier series of functions of generalized bounded variation*, Studia Math.**44**(1972), 107-117. MR**0310525 (46:9623)****[8]**-,*On the summability of Fourier series of functions of*-*bounded variation*, Studia Math.**55**(1976), 97-109.**[9]**-,*On*-*bounded variation*, Studia Math.**57**(1976), 33-45. MR**0417355 (54:5408)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
26A45

Retrieve articles in all journals with MSC: 26A45

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1979-0521883-X

Article copyright:
© Copyright 1979
American Mathematical Society