Symmetric integrals and trigonometric series
George Elliot Cross ; Brian Sheriff Thomson
GDML_Books, (1992), p.

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...............................................................................................48

1991 Mathematics Subject Classification: Primary 26A24, 26A39, 26A45; Secondary 42A24.

EUDML-ID : urn:eudml:doc:219320 
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     author = {George Elliot Cross and Brian Sheriff Thomson},
     title = {Symmetric integrals and trigonometric series},
     series = {GDML\_Books},
     publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
     address = {Warszawa},
     year = {1992},
     zbl = {0785.26006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.dl-catalog-86ac72d8-3160-4281-8386-423c865281bc}
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George Elliot Cross; Brian Sheriff Thomson. Symmetric integrals and trigonometric series. GDML_Books (1992),  http://gdmltest.u-ga.fr/item/bwmeta1.element.dl-catalog-86ac72d8-3160-4281-8386-423c865281bc/