Complex Anal. Oper. Theory Complex Analysis https://doi.org/10.1007/s11785-018-0807-4 and Operator Theory Frame of Exponentials Related to Analytic Families Operators and Application to a Non-self Adjoint Problem of Radiation of a Vibrating Structure in a Light Fluid 1 2 Salma Charﬁ · Hanen Ellouz Received: 9 January 2018 / Accepted: 26 May 2018 © Springer International Publishing AG, part of Springer Nature 2018 Abstract In the present paper, we investigate under sufﬁcient conditions the existence of frames of exponential families, where the exponents coincide with the eigenvalues of the perturbed operator 2 k T (ε) := T + εT + ε T + ··· + ε T + ··· ,ε ∈ C. 0 1 2 k Here T is a closed densely deﬁned linear operator on a separable Hilbert space H with domain D(T ) having isolated eigenvalues with multiplicity one and T , T ,... are 0 1 2 linear operators on H having the same domain D ⊃ D(T ) and satisfying a speciﬁc growing inequality. The obtained results are applied to a non-self adjoint problem deduced from a perturbation method for sound radiation. Keywords Frames of exponentials · Eigenvalues · Elastic membrane · Integro- differential operator Communicated by
Complex Analysis and Operator Theory – Springer Journals
Published: Jun 5, 2018
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera