JNCA: The best constant of Sobolev inequality corresponding to antiperiodic boundary value problem for (-1)M(d/dx)2M



	Volume 10, Number 1, April 2009, pp. 103-116
Hiroyuki Yamagishi, Yoshinori Kametaka and Atsushi Nagai
Key words:
Sobolev inequality, best constant, Green function, reproducing kernel, Bernoulli polynomial, Riemann zeta function.
Mathematices Subject Classification: Primary 34B27, Secondary 46E35.

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	Abstract:
	The variational meaning of the special values ζ(2M ) (M =1,2,3, ...) of Riemann zeta function ζ(s) is clarified. They are essentially the best constant of Sobolev inequality, which is given explicitly by investigating Green function of the ``antiperiodic'' boundary value problem for differential operator (-1)^M(d/dx)²^M.

The best constant of Sobolev inequality corresponding to antiperiodic boundary value problem for (-1)^M(d/dx)^2M