科研之友
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摘要
A theory of summability of orthonormal sets is introduced in multinormed spaces. The approach which is presented caters for infinite sets {phi(j)}(j is an element of J), where the index set J may be uncountable, and is applied to obtain convergence results in appropriate spaces of test functions and corresponding spaces of generalized functions. These spaces are constructed in a systematic manner that relies heavily on properties of orthonormal bases in Hilbert spaces. A space of almost-periodic generalized functions, in which each generalized function can be expanded in terms of an uncountable basis of exponential functions, is obtained as a special case of our theory.
- 出版日期2013
