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The spectral function and principal eigenvalues for Schrodinger operators

Abstract:
Let m ∈ L1 loc (ℝN), 0 ≠ m+ in Kato's class. We investigate the spectral function λ rarr; s(Δ + λm) where s(Δ + λm) denotes the upper bound of the spectrum of the Schrödinger operator Δ + λm. In particular, we determine its derivative at 0. If m- is sufficiently large, we show that there exists a unique λ1 > 0 such that s(Δ + λ1m) = 0. Under suitable conditions on m+ it follows that 0 is an eigenvalue of Δ + λ1m with positive eigenfunction.
Publication status:
Published

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Publisher copy:
10.1023/A:1017928532615

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Journal:
POTENTIAL ANALYSIS
Volume:
7
Issue:
1
Pages:
415-436
Publication date:
1997-08-05
DOI:
ISSN:
0926-2601
URN:
uuid:b94e793b-5bbd-43bc-88dc-fc82db40aa0c
Source identifiers:
26514
Local pid:
pubs:26514

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