TY  - JOUR
ID  - Yakubovich2009
LB  - Yakubovich2009
AU  - Yakubovich, Semyon B.
TI  - Beurling's theorems and inversion formulas for certain index transforms
ST  - Beurling's theorems and inversion formulas for certain index transforms
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2009
VL  - 29
IS  - 1
SP  - 93
EP  - 110
DO  - http://dx.doi.org/10.7494/OpMath.2009.29.1.93
UR  - http://dx.doi.org/10.7494/OpMath.2009.29.1.93
AB  - The familiar Beurling theorem (an uncertainty principle), which is known for the Fourier transform pairs, has recently been proved by the author for the Kontorovich-Lebedev transform. In this paper analogs of the Beurling theorem are established for certain index transforms with respect to a parameter of the modified Bessel functions. In particular, we treat the generalized Lebedev-Skalskaya transforms, the Lebedev type transforms involving products of the Macdonald functions of different arguments and an index transform with the Nicholson kernel function. We also find inversion formulas for the Lebedev-Skalskaya operators of an arbitrary index and the Nicholson kernel transform.
KW  - Beurling theorem
KW  - Kontorovich-Lebedev transform
KW  - Lebedev-Skalskaya transforms
KW  - Fourier transform
KW  - Laplace transform
KW  - modified Bessel functions
KW  - uncertainty principle
KW  - the Nicholson function
SN  - 1232-9274
ER  -