TY - JOUR
T1 - Bateman's equation and similar units
AU - Roesler, Friedrich
PY - 1997/1/1
Y1 - 1997/1/1
N2 - The multiplication K(x, y)° ○ F(y, z) = ∫K(x, y)F(y, z) dy of real functions K and F can be interpreted as the analytic version of matrix multiplication. This suggests examining whether this multiplication has a unit element, i.e., a kernel E(x, y) such that E(x, y)○ F(y,z} = F(x, z) or ∫E(x, y)f(y) dy = f(x) for infinitely many linear independent functions f. Bateman's function [sin(x - y)]/π(x - y) is an example of such a kernel E(x, y). This paper develops a procedure to construct Bateman's function and similar units.
AB - The multiplication K(x, y)° ○ F(y, z) = ∫K(x, y)F(y, z) dy of real functions K and F can be interpreted as the analytic version of matrix multiplication. This suggests examining whether this multiplication has a unit element, i.e., a kernel E(x, y) such that E(x, y)○ F(y,z} = F(x, z) or ∫E(x, y)f(y) dy = f(x) for infinitely many linear independent functions f. Bateman's function [sin(x - y)]/π(x - y) is an example of such a kernel E(x, y). This paper develops a procedure to construct Bateman's function and similar units.
UR - http://www.scopus.com/inward/record.url?scp=0031537543&partnerID=8YFLogxK
U2 - 10.1016/0024-3795(95)00528-5
DO - 10.1016/0024-3795(95)00528-5
M3 - Article
AN - SCOPUS:0031537543
SN - 0024-3795
VL - 250
SP - 253
EP - 273
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
ER -