n-Laplacians on Metric Graphs and Almost Periodic Functions: I
Keyword(s):
AbstractThe spectra of n-Laplacian operators $$(-\Delta )^n$$ ( - Δ ) n on finite metric graphs are studied. An effective secular equation is derived and the spectral asymptotics are analysed, exploiting the fact that the secular function is close to a trigonometric polynomial. The notion of the quasispectrum is introduced, and its uniqueness is proved using the theory of almost periodic functions. To achieve this, new results concerning roots of functions close to almost periodic functions are proved. The results obtained on almost periodic functions are of general interest outside the theory of differential operators.
1978 ◽
Vol 33
(2)
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pp. 1-52
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Keyword(s):
Compact Families of Almost Periodic Functions and an Application of the Schauder Fixed-Point Theorem
1969 ◽
Vol 17
(6)
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pp. 1258-1262
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1996 ◽
Vol 452
(1953)
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pp. 2263-2277
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1969 ◽
Vol 72
(4)
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pp. 345-353
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2018 ◽
Vol 14
(09)
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pp. 2343-2368
1934 ◽
Vol 36
(3)
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pp. 445-445
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