On Certain Functional Identities in EN
Canadian journal of mathematics, Tome 23 (1971) no. 2, pp. 315-324
Voir la notice de l'article provenant de la source Cambridge University Press
1. If f is a real-valued function possessing a Taylor series convergent in (a — R, a + R), then it satisfies the following operational identity 1.1 in which D 2 = d 2/du 2. Furthermore, when g is a solution of y′′ + λ 2 y = 0 in (a – R, a + R), then g is such a function and (1.1) specializes to 1.2 In this note we generalize these results to the real Euclidean space EN , our conclusions being Theorems 1 and 2 below. Clearly, (1.2) is a special case of (1.1) but in higher-dimensional space it is of interest to allow g, now a solution of 1.3 to possess singularities at isolated points away from the origin. It is then necessary to consider not only a neighbourhood of the origin but annular regions also.
Mercer, A. McD. On Certain Functional Identities in EN. Canadian journal of mathematics, Tome 23 (1971) no. 2, pp. 315-324. doi: 10.4153/CJM-1971-031-1
@article{10_4153_CJM_1971_031_1,
author = {Mercer, A. McD.},
title = {On {Certain} {Functional} {Identities} in {EN}},
journal = {Canadian journal of mathematics},
pages = {315--324},
year = {1971},
volume = {23},
number = {2},
doi = {10.4153/CJM-1971-031-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1971-031-1/}
}
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