Geodesic
Unbounded Transforms and Approximation of Functions over $p$-adic Fields
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of mathematical physics and $p$-adic analysis, Tome 265 (2009), pp. 220-228

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We consider functions of a $p$-adic variable with values in different spaces. In each case we consider an unbounded integral operator and a corresponding issue. More precisely, we study the Riesz–Volkenborn integral representation of functions with values in a non-Archimedean field, the Vladimirov operator and corresponding vectors of exponential type in spaces of complex-valued functions, and the Fourier transform and its (dis)continuity in spaces of Banach-valued functions. 
@article{TM_2009_265_a18,
     author = {A. Radyna and Ya. Radyna and Ya. Radyno},
     title = {Unbounded {Transforms} and {Approximation} of {Functions} over $p$-adic {Fields}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {220--228},
     publisher = {mathdoc},
     volume = {265},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2009_265_a18/}
}
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A. Radyna; Ya. Radyna; Ya. Radyno. Unbounded Transforms and Approximation of Functions over $p$-adic Fields. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of mathematical physics and $p$-adic analysis, Tome 265 (2009), pp. 220-228. http://geodesic.mathdoc.fr/item/TM_2009_265_a18/