Einar Hille’s scientific contributions

... The study of approximately subadditive and higher order subadditive functions, discovering the linkage of subadditive function with convex and periodic functions, several important limit theorems have been investigated in the last few decades. The detailed research can be found in the papers [1][2][3][4][5][6][7][8][9][10] and the reference therein. ...

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Revisiting Fekete’s Lemma, Subadditive and Periodic Sequences

... In operator theory on separable Hilbert spaces, the major problem with integration for operator-valued functions is that these functions need not have a Lebesgue (like) integral. However, they always have a HK-integral (see [42]). ...

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On the Four Dimensional-Forward Difference Matrix

... Gâteaux differentials of S. Let us go back to the direct scattering problem. The functions W φ N [y 3 , · · · , y N ] mentioned above can be used to express higher order Gâteaux differentials of S at 0. In this paper, we define higher order Gâteaux differentiability as follows (see, e.g., [5,6]): For Banach spaces X , Y, an open set U ⊂ X , a mapping F : U → Y and N ∈ N, we say that F is N-th order Gâteaux differentiable as a mapping from U to Y if for any ϕ 0 ∈ U and ϕ 1 ∈ X , the vector ...

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On inverse scattering for the two-dimensional nonlinear Klein-Gordon equation