Семинар на 27.09.2018 г.

На 27 септември 2018 г. /четвъртък/ от 13:15 часа в зала 300 на ИЯИЯЕ Тодор Тодоров (Сан Луис Обиспо, Калифорния, САЩ) ще изнесе доклад на тема:

" Infinite-Dimensional Linear Algebra and Solvability of Linear Partial Differential Equations".

Резюме:

We prove the solvability a class of linear partial di↵erential equations with smooth coefficients of the form P(x,δ)U = T within the algebraic dual ∗D(Ω) of the space of test functions D(Ω). In other words, we prove the surjectivity of a class of operators (called regular ) P(x,δ) on ∗D(Ω).

The result is (we believe) of interest, because many equations of this form (such as H. Lewy’s equation) do not have a distributional solution even for T ∈ D(Ω). Consequently, we argue that it is sometimes beneficial to use the larger framework of ∗D(Ω) rather than the more popular D′(Ω).

In the time remaining we shall discuss the algebraic background of this result: the infinite-dimensional linear algebra: a linear algebra of infinitedimensional vector spaces based on Hamel (rather than Hilbert) bases.

 

 

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