On the Mehler-Fock transform in \(L_ p\)-space. (English) Zbl 0873.44002
The authors investigate certain mapping properties of the Mehler-Fock transform, introduced by P. G. Mehler [Math. Ann. 18, 161-194 (1881)], defined by the integral
\[
{\mathcal M}{\mathcal F}[f](\tau)= {\pi\over 2} \int^\infty_0 P_{-1/2+i\tau/2}(2y^2+ 1)f(y)dy,\quad \tau>0,
\]
where \(P_v(z)\) is the Legendre function of the first kind of index \(v\) and \(f\in L_p(\mathbb{R}_+)\).
Reviewer: Ram Kishore Saxena (Jodhpur)
MSC:
| 44A15 | Special integral transforms (Legendre, Hilbert, etc.) |
References:
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