Weighted approximation of entire functions of exponential type of several variables by trigonometric polynomials

Letf be an entire function (in Cⁿ) of exponential type for whichf(x)=0(?(x)) on the real subspace (mathbb{R}^w (phi geqslant 1,{mathbf{ }}mathop {lim }limits_{left| x right| to infty } phi (x) = infty )) and ?δ>0?C_δ>0 $$left| {f(z)} right| leqslant C_delta exp left{ {h_s (y) + Sleft| z right|} right},z = x + iy$$ where h, (x)=sup〈3, x〉, S being a convex set in ?ⁿ. Then for any ?, ?>0, the functionf can be approximated with any degree of accuracy in the form p→ (mathop {sup }limits_{x in mathbb{R}^w } frac{{left| {P(x)} right|}}{{varphi (x)}}) by linear combinations of functions x→expi〈λx〉 with frequenciesX belonging to an ?-neighborhood of the set S.