Djakov, P. B.; Mityagin, B. S. Spectral triangles of non-selfadjoint Hill and Dirac operators. (English. Russian original) Zbl 07281941 Russ. Math. Surv. 75, No. 4, 587-626 (2020); translation from Usp. Mat. Nauk 75, No. 4, 3-44 (2020). MSC: 47E05 34L40 34L10 PDFBibTeX XMLCite \textit{P. B. Djakov} and \textit{B. S. Mityagin}, Russ. Math. Surv. 75, No. 4, 587--626 (2020; Zbl 07281941); translation from Usp. Mat. Nauk 75, No. 4, 3--44 (2020) Full Text: DOI
Anahtarci, Berkay; Djakov, Plamen Asymptotics of spectral gaps of 1D Dirac operator whose potential is a linear combination of two exponential terms. (English) Zbl 1317.81118 Asymptotic Anal. 92, No. 1-2, 141-160 (2015). MSC: 81Q10 34L40 34L20 PDFBibTeX XMLCite \textit{B. Anahtarci} and \textit{P. Djakov}, Asymptotic Anal. 92, No. 1--2, 141--160 (2015; Zbl 1317.81118) Full Text: DOI arXiv
Djakov, Plamen B.; Mityagin, Boris Samuilovich Riesz basis property of Hill operators with potentials in weighted spaces. (English. Russian original) Zbl 1369.47055 Trans. Mosc. Math. Soc. 2014, 151-172 (2014); translation from Tr. Mosk. Mat. O.-va 75, No. 2, 181-204 (2014). MSC: 47E05 34L40 34L10 PDFBibTeX XMLCite \textit{P. B. Djakov} and \textit{B. S. Mityagin}, Trans. Mosc. Math. Soc. 2014, 151--172 (2014; Zbl 1369.47055); translation from Tr. Mosk. Mat. O.-va 75, No. 2, 181--204 (2014) Full Text: DOI arXiv
Djakov, Plamen; Mityagin, Boris Combinatorial identities related to eigen-function decompositions of Hill operators: open questions. (English) Zbl 1276.47058 Integral Equations Oper. Theory 75, No. 1, 7-12 (2013). Reviewer: Meirong Zhang (Beijing) MSC: 47E05 34L40 34L10 05A19 00A07 PDFBibTeX XMLCite \textit{P. Djakov} and \textit{B. Mityagin}, Integral Equations Oper. Theory 75, No. 1, 7--12 (2013; Zbl 1276.47058) Full Text: DOI arXiv
Djakov, Plamen; Mityagin, Boris Riesz bases consisting of root functions of 1D Dirac operators. (English) Zbl 1297.47046 Proc. Am. Math. Soc. 141, No. 4, 1361-1375 (2013). MSC: 47E05 34L40 34L10 PDFBibTeX XMLCite \textit{P. Djakov} and \textit{B. Mityagin}, Proc. Am. Math. Soc. 141, No. 4, 1361--1375 (2013; Zbl 1297.47046) Full Text: DOI arXiv
Anahtarci, Berkay; Djakov, Plamen Refined asymptotics of the spectral gap for the Mathieu operator. (English) Zbl 1256.34078 J. Math. Anal. Appl. 396, No. 1, 243-255 (2012). Reviewer: Rodica Luca Tudorache (Iaşi) MSC: 34L20 34B08 34L40 PDFBibTeX XMLCite \textit{B. Anahtarci} and \textit{P. Djakov}, J. Math. Anal. Appl. 396, No. 1, 243--255 (2012; Zbl 1256.34078) Full Text: DOI arXiv
Djakov, Plamen; Mityagin, Boris Equiconvergence of spectral decompositions of 1D Dirac operators with regular boundary conditions. (English) Zbl 1258.34174 J. Approx. Theory 164, No. 7, 879-927 (2012). Reviewer: Chuan-Fu Yang (Nanjing) MSC: 34L40 34L10 41A30 47A75 PDFBibTeX XMLCite \textit{P. Djakov} and \textit{B. Mityagin}, J. Approx. Theory 164, No. 7, 879--927 (2012; Zbl 1258.34174) Full Text: DOI arXiv
Djakov, Plamen; Mityagin, Boris 1D Dirac operators with special periodic potentials. (English) Zbl 1256.47029 Bull. Pol. Acad. Sci., Math. 60, No. 1, 59-75 (2012). Reviewer: Miyeon Kwon (Platteville) MSC: 47E05 34L40 PDFBibTeX XMLCite \textit{P. Djakov} and \textit{B. Mityagin}, Bull. Pol. Acad. Sci., Math. 60, No. 1, 59--75 (2012; Zbl 1256.47029) Full Text: DOI arXiv
Djakov, Plamen; Mityagin, Boris Convergence of spectral decompositions of Hill operators with trigonometric polynomial potentials. (English) Zbl 1367.47050 Math. Ann. 351, No. 3, 509-540 (2011). MSC: 47E05 34L40 34L10 PDFBibTeX XMLCite \textit{P. Djakov} and \textit{B. Mityagin}, Math. Ann. 351, No. 3, 509--540 (2011; Zbl 1367.47050) Full Text: DOI arXiv
Djakov, P.; Mityagin, B. Bari-Markus property for Riesz projections of 1D periodic Dirac operators. (English) Zbl 1198.34188 Math. Nachr. 283, No. 3, 443-462 (2010). Reviewer: Vassilis G. Papanicolaou (Athena) MSC: 34L40 47B06 47E05 PDFBibTeX XMLCite \textit{P. Djakov} and \textit{B. Mityagin}, Math. Nachr. 283, No. 3, 443--462 (2010; Zbl 1198.34188) Full Text: DOI arXiv
Djakov, Plamen; Mityagin, Boris Bari-Markus property for Riesz projections of Hill operators with singular potentials. (English) Zbl 1185.34130 Aytuna, Aydin (ed.) et al., Functional analysis and complex analysis. International conference, Istanbul, Turkey, September 17–21, 2007. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4460-1/pbk). Contemporary Mathematics 481, 59-80 (2009). Reviewer: Vassilis G. Papanicolaou (Athena) MSC: 34L40 47B06 47E05 PDFBibTeX XMLCite \textit{P. Djakov} and \textit{B. Mityagin}, Contemp. Math. 481, 59--80 (2009; Zbl 1185.34130) Full Text: arXiv
Djakov, P.; Mityagin, B. Spectral gap asymptotics of one-dimensional Schrödinger operators with singular periodic potentials. (English) Zbl 1176.34108 Integral Transforms Spec. Funct. 20, No. 3-4, 265-273 (2009). Reviewer: Vassilis G. Papanicolaou (Athena) MSC: 34L20 34L40 47E05 34B30 PDFBibTeX XMLCite \textit{P. Djakov} and \textit{B. Mityagin}, Integral Transforms Spec. Funct. 20, No. 3--4, 265--273 (2009; Zbl 1176.34108) Full Text: DOI
Djakov, P.; Mityagin, B. S. Instability zones of periodic 1-dimensional Schrödinger and Dirac operators. (English. Russian original) Zbl 1128.47041 Russ. Math. Surv. 61, No. 4, 663-766 (2006); translation from Usp. Mat. Nauk 61, No. 4, 77-182 (2006). Reviewer: Vassilis G. Papanicolaou (Athena) MSC: 47E05 34L40 34L20 PDFBibTeX XMLCite \textit{P. Djakov} and \textit{B. S. Mityagin}, Russ. Math. Surv. 61, No. 4, 663--766 (2006; Zbl 1128.47041); translation from Usp. Mat. Nauk 61, No. 4, 77--182 (2006) Full Text: DOI
Djakov, Plamen; Mityagin, Boris Instability zones of a periodic 1D Dirac operator and smoothness of its potential. (English) Zbl 1083.34064 Commun. Math. Phys. 259, No. 1, 139-183 (2005). Reviewer: Agostino Prástaro (Roma) MSC: 34L40 47E05 81Q05 PDFBibTeX XMLCite \textit{P. Djakov} and \textit{B. Mityagin}, Commun. Math. Phys. 259, No. 1, 139--183 (2005; Zbl 1083.34064) Full Text: DOI
Djakov, Plamen; Mityagin, Boris Simple and double eigenvalues of the Hill operator with a two-term potential. (English) Zbl 1080.34066 J. Approximation Theory 135, No. 1, 70-104 (2005). Reviewer: Marek S. Karaś (Kraków) (MR2151250) MSC: 34L20 34L40 47E05 PDFBibTeX XMLCite \textit{P. Djakov} and \textit{B. Mityagin}, J. Approx. Theory 135, No. 1, 70--104 (2005; Zbl 1080.34066) Full Text: DOI
Djakov, Plamen; Mityagin, Boris Multiplicities of the eigenvalues of periodic Dirac operators. (English) Zbl 1069.34128 J. Differ. Equations 210, No. 1, 178-216 (2005). Reviewer: Mihai Pascu (Bucureşti) MSC: 34L40 47E05 PDFBibTeX XMLCite \textit{P. Djakov} and \textit{B. Mityagin}, J. Differ. Equations 210, No. 1, 178--216 (2005; Zbl 1069.34128) Full Text: DOI
Djakov, Plamen; Mityagin, Boris Asymptotics of instability zones of Hill operators with a two term potential. (English) Zbl 1063.34081 C. R., Math., Acad. Sci. Paris 339, No. 5, 351-354 (2004). Reviewer: Antonio Linero Bas (Murcia) MSC: 34L40 34L20 47E05 34B30 PDFBibTeX XMLCite \textit{P. Djakov} and \textit{B. Mityagin}, C. R., Math., Acad. Sci. Paris 339, No. 5, 351--354 (2004; Zbl 1063.34081) Full Text: DOI
Djakov, Plamen; Mityagin, Boris Spectra of 1-D periodic Dirac operators and smoothness of potentials. (English) Zbl 1079.47044 C. R. Math. Acad. Sci., Soc. R. Can. 25, No. 4, 121-125 (2003). Reviewer: Pavel Dyshlovenko (Ul’yanovsk) MSC: 47E05 34L40 81Q05 PDFBibTeX XMLCite \textit{P. Djakov} and \textit{B. Mityagin}, C. R. Math. Acad. Sci., Soc. R. Can. 25, No. 4, 121--125 (2003; Zbl 1079.47044)
Djakov, Plamen; Mityagin, Boris Spectral triangles of Schrödinger operators with complex potentials. (English) Zbl 1088.34072 Sel. Math., New Ser. 9, No. 4, 495-528 (2003). MSC: 34L40 34L15 81Q10 47E05 PDFBibTeX XMLCite \textit{P. Djakov} and \textit{B. Mityagin}, Sel. Math., New Ser. 9, No. 4, 495--528 (2003; Zbl 1088.34072) Full Text: DOI
Djakov, Plamen; Mityagin, Boris The asymptotics of spectral gaps of a 1D Dirac operator with cosine potential. (English) Zbl 1046.34096 Lett. Math. Phys. 65, No. 2, 95-108 (2003). Reviewer: Eckhard Giere (Clausthal-Zellerfeld) MSC: 34L40 47E05 PDFBibTeX XMLCite \textit{P. Djakov} and \textit{B. Mityagin}, Lett. Math. Phys. 65, No. 2, 95--108 (2003; Zbl 1046.34096) Full Text: DOI
Djakov, Plamen; Mityagin, Boris Spectral gaps of the periodic Schrödinger operator when its potential is an entire function. (English) Zbl 1047.34100 Adv. Appl. Math. 31, No. 3, 562-596 (2003). Reviewer: Alan L. Andrew (Bundoora) MSC: 34L40 34L20 47E05 PDFBibTeX XMLCite \textit{P. Djakov} and \textit{B. Mityagin}, Adv. Appl. Math. 31, No. 3, 562--596 (2003; Zbl 1047.34100) Full Text: DOI
Djakov, Plamen; Mityagin, Boris Smoothness of Schrödinger operator potential in the case of Gevrey type asymptotics of the gaps. (English) Zbl 1037.34080 J. Funct. Anal. 195, No. 1, 89-128 (2002). Reviewer: Hyeona Lim (Mississippi) MSC: 34L40 47E05 PDFBibTeX XMLCite \textit{P. Djakov} and \textit{B. Mityagin}, J. Funct. Anal. 195, No. 1, 89--128 (2002; Zbl 1037.34080) Full Text: DOI