On classes of infinitely differentiable functions

The paper discusses the classes of infinitely differentiable functions, the growth of derivatives are limited given the positive sequence. This sequence can behave arbitrarily, ie be a regular, but non-zero it should be the members of an infinite number. It offers a variety of regularization of these sequences, depending on the type of area in which we study classes of infinitely differentiable functions. The class of infinitely differentiable functions, which limited the growth of the derivatives obtained regularized sequence identical to the original item by item class. It is possible to establish easily verifiable algebraic conditions for imbedding Sobolev spaces of infinite order, considered in various fields, expressed in terms of the parameters space.
Key words: regularization, the sequence space, the terms of attachment.