Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 16, Tome 138 (1984), pp. 33-34
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A. F. Vakulenko. The Hardy estimates in $\mathbb R^n$ and absence of positive eigenvalues for Schrodinger operators with complex potentials. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 16, Tome 138 (1984), pp. 33-34. http://geodesic.mathdoc.fr/item/ZNSL_1984_138_a2/
@article{ZNSL_1984_138_a2,
author = {A. F. Vakulenko},
title = {The {Hardy} estimates in $\mathbb R^n$ and absence of positive eigenvalues for {Schrodinger} operators with complex potentials},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {33--34},
year = {1984},
volume = {138},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_138_a2/}
}
TY - JOUR
AU - A. F. Vakulenko
TI - The Hardy estimates in $\mathbb R^n$ and absence of positive eigenvalues for Schrodinger operators with complex potentials
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1984
SP - 33
EP - 34
VL - 138
UR - http://geodesic.mathdoc.fr/item/ZNSL_1984_138_a2/
LA - ru
ID - ZNSL_1984_138_a2
ER -
%0 Journal Article
%A A. F. Vakulenko
%T The Hardy estimates in $\mathbb R^n$ and absence of positive eigenvalues for Schrodinger operators with complex potentials
%J Zapiski Nauchnykh Seminarov POMI
%D 1984
%P 33-34
%V 138
%U http://geodesic.mathdoc.fr/item/ZNSL_1984_138_a2/
%G ru
%F ZNSL_1984_138_a2
Using the following estimit $$ \int_{\mathbb R^n}|x|^{2p+2}|\Delta\varphi+\varphi|^2\,dx\geqslant C(p)\int_{\mathbb R^n}|x|^{2p}|\varphi|^2\,dx $$ with $C(p)\to\infty$ as $p\to\infty$, we prove the absence of $L_2$-solution of $$ \Delta\varphi+v\varphi=\varphi $$ with $|v(x)|\leqslant C(1+|x|)^{-1-\varepsilon}$.
