Totally positive refinable functions with general dilation M

2017 ◽  
Vol 112 ◽  
pp. 17-26
Author(s):  
Laura Gori ◽  
Francesca Pitolli
Keyword(s):  
Refinable Functions ◽  
Totally Positive

scholarly journals The Totally Positive Completion Problem: The 3-by-n Case

2021 ◽  
Vol 9 (1) ◽  
pp. 226-239
Author(s):  
D. Carter ◽  
K.E. DiMarco ◽  
C.R. Johnson ◽  
L. Wedemeyer ◽  
Z. Yu
Keyword(s):  
Completion Problem ◽  
Totally Positive

Abstract The 3-by-n TP-completable patterns are characterized by identifying the minimal obstructions up to natural symmetries. They are finite in number.

FINITENESS RESULTS FOR REGULAR DEFINITE TERNARY QUADRATIC FORMS OVER ${\mathbb Q}(\sqrt{5})$

2007 ◽  
Vol 03 (04) ◽  
pp. 541-556 ◽  
Author(s):  
WAI KIU CHAN ◽  
A. G. EARNEST ◽  
MARIA INES ICAZA ◽  
JI YOUNG KIM
Keyword(s):  
Quadratic Form ◽  
Number Field ◽  
Quadratic Forms ◽  
Positive Definite ◽  
Integral Quadratic Form ◽  
Ring Of Integers ◽  
Ternary Quadratic Forms ◽  
Totally Positive ◽  
Finiteness Result

Let 𝔬 be the ring of integers in a number field. An integral quadratic form over 𝔬 is called regular if it represents all integers in 𝔬 that are represented by its genus. In [13,14] Watson proved that there are only finitely many inequivalent positive definite primitive integral regular ternary quadratic forms over ℤ. In this paper, we generalize Watson's result to totally positive regular ternary quadratic forms over [Formula: see text]. We also show that the same finiteness result holds for totally positive definite spinor regular ternary quadratic forms over [Formula: see text], and thus extends the corresponding finiteness results for spinor regular quadratic forms over ℤ obtained in [1,3].

Building refinable functions from their values at integers

CALCOLO ◽  
2000 ◽  
Vol 37 (3) ◽  
pp. 139-158 ◽  
Author(s):  
Johan M. de Villiers ◽  
Charles A. Micchelli ◽  
Thomas Sauer
Keyword(s):  
Refinable Functions

scholarly journals The regularity of refinable functions

2013 ◽  
Vol 34 (1) ◽  
pp. 142-147
Author(s):  
Yang Wang ◽  
Zhiqiang Xu
Keyword(s):  
Refinable Functions

scholarly journals Totally positive functions through nonstationary subdivision schemes

2007 ◽  
Vol 200 (1) ◽  
pp. 255-265 ◽  
Author(s):  
Costanza Conti ◽  
Laura Gori ◽  
Francesca Pitolli
Keyword(s):  
Subdivision Schemes ◽  
Totally Positive ◽  
Positive Functions
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