Symmetric integrals and trigonometric series

George Elliot Cross; Brian Sheriff Thomson

  • Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1992

Abstract

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CONTENTS 1. Introduction............................................................................................5 2. Some preliminary definitions..................................................................6 3. Mařík's symmetric difference..................................................................9 4. Basic definitions...................................................................................11 5. Properties of the second symmetric variation for real functions...........15 6. Measure properties..............................................................................19 7. The integral.........................................................................................23 8. Additivity..............................................................................................26 9. Relations to the James P²-integral.......................................................2710. Relations to the Burkill SCP-integral...................................................2911. Mařík's integration by parts formula....................................................3612. Burkill's integration by parts formula...................................................3913. An application to trigonometric series.................................................4314. Some further applications...................................................................47References...............................................................................................481991 Mathematics Subject Classification: Primary 26A24, 26A39, 26A45; Secondary 42A24.

How to cite

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George Elliot Cross, and Brian Sheriff Thomson. Symmetric integrals and trigonometric series. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1992. <http://eudml.org/doc/219320>.

@book{GeorgeElliotCross1992,
abstract = {CONTENTS 1. Introduction............................................................................................5 2. Some preliminary definitions..................................................................6 3. Mařík's symmetric difference..................................................................9 4. Basic definitions...................................................................................11 5. Properties of the second symmetric variation for real functions...........15 6. Measure properties..............................................................................19 7. The integral.........................................................................................23 8. Additivity..............................................................................................26 9. Relations to the James P²-integral.......................................................2710. Relations to the Burkill SCP-integral...................................................2911. Mařík's integration by parts formula....................................................3612. Burkill's integration by parts formula...................................................3913. An application to trigonometric series.................................................4314. Some further applications...................................................................47References...............................................................................................481991 Mathematics Subject Classification: Primary 26A24, 26A39, 26A45; Secondary 42A24.},
author = {George Elliot Cross, Brian Sheriff Thomson},
keywords = {variational measure; -integral of James; second order symmetric derivative; symmetric Cesàro derivative; trigonometric series; Fourier series; SCP-integral of Burkill},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Symmetric integrals and trigonometric series},
url = {http://eudml.org/doc/219320},
year = {1992},
}

TY - BOOK
AU - George Elliot Cross
AU - Brian Sheriff Thomson
TI - Symmetric integrals and trigonometric series
PY - 1992
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - CONTENTS 1. Introduction............................................................................................5 2. Some preliminary definitions..................................................................6 3. Mařík's symmetric difference..................................................................9 4. Basic definitions...................................................................................11 5. Properties of the second symmetric variation for real functions...........15 6. Measure properties..............................................................................19 7. The integral.........................................................................................23 8. Additivity..............................................................................................26 9. Relations to the James P²-integral.......................................................2710. Relations to the Burkill SCP-integral...................................................2911. Mařík's integration by parts formula....................................................3612. Burkill's integration by parts formula...................................................3913. An application to trigonometric series.................................................4314. Some further applications...................................................................47References...............................................................................................481991 Mathematics Subject Classification: Primary 26A24, 26A39, 26A45; Secondary 42A24.
LA - eng
KW - variational measure; -integral of James; second order symmetric derivative; symmetric Cesàro derivative; trigonometric series; Fourier series; SCP-integral of Burkill
UR - http://eudml.org/doc/219320
ER -

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