TY - JOUR

T1 - Functions on noncompact lie groups with positive fourier transforms

AU - Kawazoe, Takeshi

PY - 1995/5

Y1 - 1995/5

N2 - Let G be a homogeneous group with the graded Lie algebra or a noncompact semisimple Lie group with finite center. We define the Fourier transform f of f as a family of operators, and we say that f is positive if all f(n) are positive. Then, we construct an integrable function f on G with positive f and the restriction of f to any ball centered at the origin of G is square-integrable, however, f is not square-integrable on G.

AB - Let G be a homogeneous group with the graded Lie algebra or a noncompact semisimple Lie group with finite center. We define the Fourier transform f of f as a family of operators, and we say that f is positive if all f(n) are positive. Then, we construct an integrable function f on G with positive f and the restriction of f to any ball centered at the origin of G is square-integrable, however, f is not square-integrable on G.

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U2 - 10.1090/S0002-9939-1995-1277119-7

DO - 10.1090/S0002-9939-1995-1277119-7

M3 - Article

AN - SCOPUS:0346576049

SN - 0002-9939

VL - 123

SP - 1411

EP - 1415

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 5

ER -