THEORY OF REPRODUCING KERNELS
THEORY OF REPRODUCING KERNELS
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DOI：
10.1090/s0002-9947-1950-0051437-7
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发表时间：
1950-01-01
影响因子：
1.3
通讯作者：
ARONSZAJN, N
中科院分区：
文献类型：
--
作者：
ARONSZAJN, N
这篇论文可以看作是我们上一篇发表在《剑桥哲学学会学报》上的论文的续篇，这篇论文写于1942-1943年，发表在《Theorie gsamnsamrale de noyaux reproduction - premiurere party》（vol. 39(1944)）。在本文的导言中，我们概述了接下来的论文计划。然而，与此同时，一般理论在许多方面都得到了发展，我们原来的计划不得不改变。在写第一篇论文的时候，由于战时的条件，我们无法考虑到所有早期的调查，尽管有时性质完全不同，但却与我们的主题有关。我们的研究涉及一种特殊类型的核，它在数学研究的许多领域以不同的名称和不同的方式被使用。因此，我们将以一个简短的历史介绍开始我们的论文，其中我们将试图指出不同的研究者使用这些核的不同方式，并澄清术语。我们还将讨论这些内核应用的更重要的趋势，但是，我们不打算对这个主题做一个完整的参考书目。在第一部分中，我们将简要讨论我们上一篇论文的基本概念和结果，并以抽象形式进一步发展这一理论。在第二部分中，我们将通过一系列例子来说明第一部分中得到的结果，这些例子将给出该理论已知应用的新发展，以及一些新的应用。
The present paper may be considered as a sequel to our previous paper in the Proceedings of the Cambridge Philosophical Society, Theorie générale de noyaux reproduisants—Première partie (vol. 39 (1944)) which was written in 1942-1943. In the introduction to this paper we outlined the plan of papers which were to follow. In the meantime, however, the general theory has been developed in many directions, and our original plans have had to be changed. Due to wartime conditions we were not able, at the time of writing the first paper, to take into account all the earlier investigations which, although sometimes of quite a different character, were, nevertheless, related to our subject.Our investigation is concerned with kernels of a special type which have been used under different names and in different ways in many domains of mathematical research. We shall therefore begin our present paper with a short historical introduction in which we shall attempt to indicate the different manners in which these kernels have been used by various investigators, and to clarify the terminology. We shall also discuss the more important trends of the application of these kernels without attempting, however, a complete bibliography of the subject matter. In Part I, we shall discuss briefly the essential notions and results of our previous paper and give a further development of the theory in an abstract form. In Part II, we shall illustrate the results obtained in the first part by a series of examples which will give new developments of already known applications of the theory, as well as some new applications.