The Fourier transform truncated on [-c,c] is usually analyzed when acting on L^2(-1/b,1/b) and its right-singular vectors are the prolate spheroidal wave functions. This paper considers the operator acting on the larger space L^2(exp(b|.|)) on which it remains injective. We give nonasymptotic upper and lower bounds on the singular values with similar qualitative behavior in m (the index), b, and c. The lower bounds are used to obtain rates of convergence for stable analytic continuation of possibly nonbandlimited functions whose Fourier transform belongs to L^2(exp(b|.|)). We also derive bounds on the sup-norm of the singular functions. Finally, we propose a numerical method to compute the SVD and apply it to stable analytic continuation when the function is observed with error on an interval.

翻译：在 [-c,c] 上拖动的Fourier变形通常在对 L2 (-1/b,1/b) 采取行动时进行分析,其右螺旋矢量是 prolate 类人造波函数。 本文认为操作者在更大的 L2 (Exp (b ⁇ ) ⁇ ) 上操作, 仍然对它进行注射。 我们给单数值上下限提供非不设防的不设防线, 其质量行为在 m( 指数)、 b 和 c 上下限, 使用下限来获取趋同率, 以稳定地继续分析 Fourier 变换为 L2( 2( exp (b ⁇. ⁇ ) 的无带限制函数。 我们还从单函数的 supp- norm 上划线。 最后, 我们提出一个计算 SVD 的数值方法, 当观察到函数时, 当一个间隔有误差时, 将其应用于稳定的解析持续 。