. . "Refinable functions"@en . _:bnode7authoritiessubjectssh2006006686 . _:bnode7authoritiessubjectssh2006006686 _:bnode8authoritiessubjectssh2006006686 . _:bnode7authoritiessubjectssh2006006686 . _:bnode8authoritiessubjectssh2006006686 . _:bnode8authoritiessubjectssh2006006686 "Refinable functions"@en . . . . . . . _:bnode17authoritiessubjectssh2006006686 . _:bnode17authoritiessubjectssh2006006686 . _:bnode17authoritiessubjectssh2006006686 "Work cat.: De Villiers, J. Building refinable functions from their values at integers, 1999." . _:bnode17authoritiessubjectssh2006006686 "found" . _:bnode23authoritiessubjectssh2006006686 . _:bnode23authoritiessubjectssh2006006686 . _:bnode23authoritiessubjectssh2006006686 "Wikipedia, via WWW, Aug. 12, 2006" . _:bnode23authoritiessubjectssh2006006686 "(Refinable function -- In mathematics, in the area of wavelet analysis, a refinable function is a function that fulfills some kind of self-similarity)"@en . _:bnode23authoritiessubjectssh2006006686 "found" . _:bnode31authoritiessubjectssh2006006686 . _:bnode31authoritiessubjectssh2006006686 . _:bnode31authoritiessubjectssh2006006686 "Fornberg, B. Modeling in applied mathematics, via WWW, Sept. 5, 2006" . _:bnode31authoritiessubjectssh2006006686 "(In general a refinable function is a function that can be written as a linear combination of squashed and shifted versions of itself)"@en . _:bnode31authoritiessubjectssh2006006686 "found" . _:bnode39authoritiessubjectssh2006006686 . _:bnode39authoritiessubjectssh2006006686 . _:bnode39authoritiessubjectssh2006006686 "Berglnd [i.e. Berglund], N. Reconstructing refinable functions, via WWW, Aug. 12, 2006" . _:bnode39authoritiessubjectssh2006006686 "(A refinable function is a function that is equal to the sum of scaled copies of itself, where the copies are contracted horizontally by 1/2, shifted left or right by multiples of 1/2 and scaled by real numbers)"@en . _:bnode39authoritiessubjectssh2006006686 "found" . _:bnode47authoritiessubjectssh2006006686 . _:bnode47authoritiessubjectssh2006006686 . _:bnode47authoritiessubjectssh2006006686 "MathWorld, via WWW, Sept. 5, 2006;Glossary of mathematical terms, via WWW, Sept. 5, 2006;Dictionary of applied math for engineers and scientists, 2003;James, R.C. Mathematics dictionary, 1992;Encylopedic dictionary of mathematics, 1987;The Penguin dictionary of mathematics, 1989" . _:bnode47authoritiessubjectssh2006006686 "notfound" . _:bnode53authoritiessubjectssh2006006686 . _:bnode53authoritiessubjectssh2006006686 . _:bnode53authoritiessubjectssh2006006686 "2006-11-09T00:00:00"^^ . _:bnode53authoritiessubjectssh2006006686 "new"^^ . _:bnode53authoritiessubjectssh2006006686 . _:bnode53authoritiessubjectssh2006006686 . _:bnode61authoritiessubjectssh2006006686 . _:bnode61authoritiessubjectssh2006006686 . _:bnode61authoritiessubjectssh2006006686 "2006-11-10T07:52:25"^^ . _:bnode61authoritiessubjectssh2006006686 "revised"^^ . _:bnode61authoritiessubjectssh2006006686 . _:bnode61authoritiessubjectssh2006006686 .