Theory and application of Fourier analysis

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Some of our important research results are as follows:1. We established a general theorem on the generalized absolute Norlund summability of orthogonal series which contains some theorems on the absolute Norlund summability and the Riesz suinmability of orthogonal series.2. We studied carefully about equivalence of the convergence of filters on a topological space and the convergence of nets in the space, ffe summarized the equivalence transparently as it is convenient in arguments in analysis.3. The point of solvability for H∞ control problems is the existence of a non-negative definite solution to the associated algebraic Riccati equation. The uniqueness of the above solution is proved for general plants in both continuous-time and discrete-time systems.4. The two convergence theorems of martingales in the limit, i. e. L1-boundedness and integrability of stopped process, are compared, and it is found that the earlier would imply the late. We gave a proof that some sequence of letters … More is qubic-free.5. A type of Strassen's theorem for the existence of probability measures with given marginals is extended to positive vector measures with values in the dual of a barred locally convex space which has certain order conditions.6. By an essential use of the Bartle bilinear integration, it is shown that the injective tensorproduct of positive vector measures in certain Banach lattices, is jointly continuous with respect to the weak convergence of vector measures.7. We discuss the semi-Riemannian submersion with affine connection and seek its fundamental equations. We define the another almost complex structure ( resp. almost contact structure ) and an indefinite Kahlerian ( resp. Sasakian) manifold with affine connection, moreover we consider the case which the total space admits these structures.8. We study on the Riemannian submersionwith α-connection, We show that if the total space is of an n-dimensional normal distribution, then the base space is of positive definite symmetric matrices of order n, the horizontal distribution is integrable and each fiber is α-flat. Also, we discuss geodesic equations on the statistical model of the multinariate normal distribution. Less