- Tytuł:
- Eigenvalue-eigenfunction problem for Steklovs smoothing operator and differential-difference equations of mixed type
- Autorzy:
-
Iakovlev, S. I.
Iakovleva, V. - Powiązania:
- https://bibliotekanauki.pl/articles/254795.pdf
- Data publikacji:
- 2013
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
Steklov's smoothing operator
spectrum
eigenvalues
eigenfunctions
mixed-type differential-difference equations
initial function
method of steps
countably normed space
transformation group
generator - Opis:
- It is shown that any μ ∈ C is an infinite multiplicity eigenvalue of the Steklov smoothing operator Sh acting on the space [formula]. For μ ≠ 0 the eigenvalue-eigenfunction problem leads to studying a differential-difference equation of mixed type. An existence and uniqueness theorem is proved for this equation. Further a transformation group is defined on a countably normed space of initial functions and the spectrum of the generator of this group is studied. Some possible generalizations are pointed out.
- Źródło:
-
Opuscula Mathematica; 2013, 33, 1; 81-98
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł