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- W2138838517 abstract "Certain classes of analytic functions in tube domains<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$T^C = mathbb{R}^n + iC$><mml:msup><mml:mi>T</mml:mi><mml:mi>C</mml:mi></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mi>ℝ</mml:mi><mml:mi>n</mml:mi></mml:msup><mml:mo>+</mml:mo><mml:mi>i</mml:mi><mml:mi>C</mml:mi></mml:math>in<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$n$><mml:mi>n</mml:mi></mml:math>-dimensional complex space, where<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$C$><mml:mi>C</mml:mi></mml:math>is an open connected cone in<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$mathbb{R}^n $><mml:msup><mml:mi>ℝ</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:math>, are studied. We show that the functions have a boundedness property in the strong topology of the space of tempered distributions<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=${g'}$><mml:msup><mml:mi>g</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:math>. We further give a direct proof that each analytic function attains the Fourier transform of its spectral function as distributional boundary value in the strong (and weak) topology of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=${g'}$><mml:msup><mml:mi>g</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:math>." @default.
- W2138838517 created "2016-06-24" @default.
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- W2138838517 date "1979-01-01" @default.
- W2138838517 modified "2023-09-25" @default.
- W2138838517 title "Strong boundedness of analytic functions in tubes" @default.
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- W2138838517 doi "https://doi.org/10.1155/s0161171279000028" @default.
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