Regular growth of systems of functions and systems of non-homogeneous convolution equations in convex domains of the complex plane

Abstract

A new method for the measurement of residual stresses in sheet materials is presented. The method is based upon the measurement of the curvature resulting from progressive removal of uniform layers from the surface of the specimen by chemical etching. The curvature is obtained from electronic speckle pattern interferograms (ESPI). As an illustration, a thin cold-rolled steel sheet was tested. Surface residual stresses were measured in as-received and heat-treated specimens. Results were found to be within the range given by x-ray diffraction measurements and show that annealing is an effective procedure for the reduction of residual stresses.

Solvability of systems of nonhomogeneous convolution equations in convex domains in $\mathbb{C}$

“…We dwell on the results of [5] in more detail. The notion of regular growth for a system of entire functions was introduced in [5]. This is a generalization of the classical notion of complete regularity of the growth for an individual entire function.…”

“…For n = 1, i.e., for one convolution equation, there are numerous publications devoted to this solvability problem; a complete solution was presented in [3,4] for the case of convex domains in the complex space of arbitrary dimension. For smooth domains, full solution of a system of nonhomogeneous convolution equations was proposed in the paper [5], where there is also a list of the most important references on the topic. We dwell on the results of [5] in more detail.…”

“…For smooth domains, full solution of a system of nonhomogeneous convolution equations was proposed in the paper [5], where there is also a list of the most important references on the topic. We dwell on the results of [5] in more detail. The notion of regular growth for a system of entire functions was introduced in [5].…”

“…This is a generalization of the classical notion of complete regularity of the growth for an individual entire function. The definition in [5] involves lower estimates of the maximal absolute values of f 1 , . .…”

“…, f n ) has regular growth. The proof of sufficiency in [5] was based on complicated induction constructions and on the solvability of cohomology groups with estimates.…”