Complete biorthogonal systems of Bessel functions
Journal Title: Математичні Студії - Year 2017, Vol 48, Issue 2
Abstract
Let ν≥−1/2 and (ρk)k∈N be a sequence of nonzero complex numbers such that ρ2k≠ρ2m for k≠m. We prove that if the system {xρk−−−√Jν(xρk):k∈N} of Bessel functions of the first kind of index ν≥−1/2 is exact (i.e. complete and minimal) in the space L2(0;1), then its biorthogonal system is also exact in L2(0;1).
Authors and Affiliations
Bohdan Vynnyts’kyi, Ruslan Khats'
Keywords
Related Articles
- EP ID EP302524
- DOI 10.15330/ms.48.2.150-155
- Views 48
- Downloads 0
On the theme of Le page
Some Le Page's commutativity criteria (in complex Banach algebras) are considered. We try to reconstruct a brief history of their evolution. Our recent results, in the real case, are also presented. These propositions ar...
Cauchy, infinitesimals and ghosts of departed quantifiers
rocedures relying on infinitesimals in Leibniz, Euler and Cauchy have been interpreted in both a Weierstrassian and Robinson’s frameworks. The latter provides closer proxies for the procedures of the classical masters. T...
Infinite-modal approximate solutions of the Bryan-Pidduck equation
Abstract The nonlinear integro-differential Bryan-Pidduck equation for a model of rough spheres is considered. An approximate solution is constructed in the form of an infinite linear combination of some Maxwellian mode...
On functions that are continuous on differentiable curves (in Ukrainian)
We prove that for a normed space X, a topological space Y, a point x0∈X, and a mapping f:X→Y, the continuity of all compositions f∘ω:[0,1]→Y at zero on differentiable curves ω:[0,1]→X with ω(0)=x0 yields the continuity o...
Composition of entire functions and bounded L-index in direction
In the present paper we give an answer to the following question: Let f:C→C be an entire function of bounded l-index, Φ:Cn→C be an entire function, n≥2, l:C→R+ be a continuous function. What are a positive continuous fun...