Rozenblum, G.; Solomyak, M. On spectral estimates for the Schrödinger operators in global dimension 2. (English) Zbl 1304.35454 St. Petersbg. Math. J. 25, No. 3, 495-505 (2014) and Algebra Anal. 25, No. 3, 185-199 (2013). MSC: 35P15 35J10 35R02 PDFBibTeX XMLCite \textit{G. Rozenblum} and \textit{M. Solomyak}, St. Petersbg. Math. J. 25, No. 3, 495--505 (2014; Zbl 1304.35454) Full Text: DOI arXiv
Laptev, Ari; Solomyak, Michael On spectral estimates for two-dimensional Schrödinger operators. (English) Zbl 1294.35048 J. Spectr. Theory 3, No. 4, 505-515 (2013). MSC: 35P20 35J10 PDFBibTeX XMLCite \textit{A. Laptev} and \textit{M. Solomyak}, J. Spectr. Theory 3, No. 4, 505--515 (2013; Zbl 1294.35048) Full Text: DOI arXiv
Solomyak, Michael On a class of spectral problems on the half-line and their applications to multi-dimensional problems. (English) Zbl 1270.34197 J. Spectr. Theory 3, No. 2, 215-235 (2013). Reviewer: Mihai Pascu (Bucureşti) MSC: 34L15 34L40 PDFBibTeX XMLCite \textit{M. Solomyak}, J. Spectr. Theory 3, No. 2, 215--235 (2013; Zbl 1270.34197) Full Text: DOI arXiv
Laptev, A.; Solomyak, M. On the negative spectrum of the two-dimensional Schrödinger operator with radial potential. (English) Zbl 1253.35037 Commun. Math. Phys. 314, No. 1, 229-241 (2012). Reviewer: Takashi Ichinose (Kanazawa) MSC: 35J10 35P20 PDFBibTeX XMLCite \textit{A. Laptev} and \textit{M. Solomyak}, Commun. Math. Phys. 314, No. 1, 229--241 (2012; Zbl 1253.35037) Full Text: DOI arXiv
Solomyak, M. Z.; Suslina, T. A.; Yafaev, D. R. On the mathematical work of M. Sh. Birman. (English. Russian original) Zbl 1236.01029 St. Petersbg. Math. J. 23, No. 1, 1-38 (2012); translation from Algebra Anal. 23, No. 1, 5-60 (2011). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 01A70 35-03 47-03 47A10 46Exx 47N20 35P25 35Q61 35Qxx PDFBibTeX XMLCite \textit{M. Z. Solomyak} et al., St. Petersbg. Math. J. 23, No. 1, 1--38 (2012; Zbl 1236.01029); translation from Algebra Anal. 23, No. 1, 5--60 (2011) Full Text: DOI
Rozenblum, G.; Solomyak, M. Spectral estimates for Schrödinger operators with sparse potentials on graphs. (English. Russian original) Zbl 1290.35284 J. Math. Sci., New York 176, No. 3, 458-474 (2011); translation from Probl. Mat. Anal. 57, 151-164 (2011). MSC: 35R02 PDFBibTeX XMLCite \textit{G. Rozenblum} and \textit{M. Solomyak}, J. Math. Sci., New York 176, No. 3, 458--474 (2011; Zbl 1290.35284); translation from Probl. Mat. Anal. 57, 151--164 (2011) Full Text: DOI arXiv
Rozenblum, G. V.; Solomyak, M. Z. On spectral estimates for Schrödinger-type operators: the case of small local dimension. (English. Russian original) Zbl 1272.47055 Funct. Anal. Appl. 44, No. 4, 259-269 (2010); translation from Funkts. Anal. Prilozh. 44, No. 4, 21-33 (2010). MSC: 47F05 35J10 35P20 35R02 PDFBibTeX XMLCite \textit{G. V. Rozenblum} and \textit{M. Z. Solomyak}, Funct. Anal. Appl. 44, No. 4, 259--269 (2010; Zbl 1272.47055); translation from Funkts. Anal. Prilozh. 44, No. 4, 21--33 (2010) Full Text: DOI arXiv
Rozenblum, Grigori; Solomyak, Michael On the spectral estimates for the Schrödinger operator on \(\mathbb Z^d\), \(d \geqslant 3\). (English. Russian original) Zbl 1207.35237 J. Math. Sci., New York 159, No. 2, 241-263 (2009); translation from Probl. Mat. Anal. 41, 107-126 (2009). Reviewer: Stepan Agop Tersian (Rousse) MSC: 35P20 39A70 35J10 PDFBibTeX XMLCite \textit{G. Rozenblum} and \textit{M. Solomyak}, J. Math. Sci., New York 159, No. 2, 241--263 (2009; Zbl 1207.35237); translation from Probl. Mat. Anal. 41, 107--126 (2009) Full Text: DOI arXiv
Friedlander, Leonid; Solomyak, Michael On the spectrum of the Dirichlet Laplacian in a narrow strip. (English) Zbl 1173.35090 Isr. J. Math. 170, 337-354 (2009). MSC: 35P15 47F05 PDFBibTeX XMLCite \textit{L. Friedlander} and \textit{M. Solomyak}, Isr. J. Math. 170, 337--354 (2009; Zbl 1173.35090) Full Text: DOI arXiv
Rozenblum, Grigori; Solomyak, Michael Counting Schrödinger boundstates: Semiclassics and beyond. (English) Zbl 1172.35046 Maz’ya, Vladimir (ed.), Sobolev spaces in mathematics II. Applications in analysis and partial differential equations. New York, NY: Springer; Novosibirsk: Tamara Rozhkovskaya Publisher (ISBN 978-0-387-85649-0/hbk; 978-0-387-85650-6/e-book; 978-0-387-85791-6/set). International Mathematical Series 9, 329-353 (2009). Reviewer: Bodo Dittmar (Halle) MSC: 35P15 35J10 PDFBibTeX XMLCite \textit{G. Rozenblum} and \textit{M. Solomyak}, in: Sobolev spaces in mathematics II. Applications in analysis and partial differential equations. New York, NY: Springer; Novosibirsk: Tamara Rozhkovskaya Publisher. 329--353 (2009; Zbl 1172.35046) Full Text: DOI arXiv
Friedlander, L.; Solomyak, M. On the spectrum of narrow periodic waveguides. (English) Zbl 1180.35392 Russ. J. Math. Phys. 15, No. 2, 238-242 (2008). MSC: 35P15 35B45 47F05 PDFBibTeX XMLCite \textit{L. Friedlander} and \textit{M. Solomyak}, Russ. J. Math. Phys. 15, No. 2, 238--242 (2008; Zbl 1180.35392) Full Text: DOI
Rozenblum, G.; Solomyak, M. On a family of differential operators with the coupling parameter in the boundary condition. (English) Zbl 1146.35064 J. Comput. Appl. Math. 208, No. 1, 57-71 (2007). Reviewer: Johannes F. Brasche (Clausthal) MSC: 35P10 47F05 47A25 PDFBibTeX XMLCite \textit{G. Rozenblum} and \textit{M. Solomyak}, J. Comput. Appl. Math. 208, No. 1, 57--71 (2007; Zbl 1146.35064) Full Text: DOI arXiv
Solomyak, M. Z. On a mathematical model of irreversible quantum graphs. (English. Russian original) Zbl 1264.47051 St. Petersbg. Math. J. 17, No. 5, 835-864 (2006); translation from Algebra Anal. 17, No. 5, 190-231 (2005). MSC: 47E05 31C20 34L40 47B25 47N50 81Q99 PDFBibTeX XMLCite \textit{M. Z. Solomyak}, St. Petersbg. Math. J. 17, No. 5, 835--864 (2006; Zbl 1264.47051); translation from Algebra Anal. 17, No. 5, 190--231 (2005) Full Text: DOI
Buslaev, V. S.; Solomyak, M. Z.; Yafaev, D. R. Mikhail Shlemovich Birman (on the occasion of his 75th birthday). (English. Russian original) Zbl 1061.01500 St. Petersbg. Math. J. 16, No. 1, 1-8 (2004); translation from Algebra Anal. 16, No. 1, 5-14 (2004). MSC: 01A70 PDFBibTeX XMLCite \textit{V. S. Buslaev} et al., St. Petersbg. Math. J. 16, No. 1, 1--8 (2004; Zbl 1061.01500); translation from Algebra Anal. 16, No. 1, 5--14 (2004) Full Text: DOI
Solomyak, Michael On approximation of functions from Sobolev spaces on metric graphs. (English) Zbl 1027.46037 J. Approximation Theory 121, No. 2, 199-219 (2003). Reviewer: Stanislaw Wedrychowicz (Rzeszów) MSC: 46E39 47B06 PDFBibTeX XMLCite \textit{M. Solomyak}, J. Approx. Theory 121, No. 2, 199--219 (2003; Zbl 1027.46037) Full Text: DOI arXiv
Sobolev, Alexander V.; Solomyak, Michael Schrödinger operators on homogeneous metric trees: spectrum in gaps. (English) Zbl 1038.81023 Rev. Math. Phys. 14, No. 5, 421-467 (2002). MSC: 81Q10 47N50 31C20 34L10 81Q15 PDFBibTeX XMLCite \textit{A. V. Sobolev} and \textit{M. Solomyak}, Rev. Math. Phys. 14, No. 5, 421--467 (2002; Zbl 1038.81023) Full Text: DOI arXiv
Naimark, K.; Solomyak, M. Eigenvalue distribution of some fractal semi-elliptic differential operators: Combinatorial approach. (English) Zbl 0983.35096 Integral Equations Oper. Theory 40, No. 4, 495-506 (2001). MSC: 35P15 28A80 PDFBibTeX XMLCite \textit{K. Naimark} and \textit{M. Solomyak}, Integral Equations Oper. Theory 40, No. 4, 495--506 (2001; Zbl 0983.35096) Full Text: DOI
Birman, M. Sh.; Solomyak, M. On the negative discrete spectrum of a periodic elliptic operator in a waveguide-type domain, perturbed by a decaying potential. (English) Zbl 1200.35196 J. Anal. Math. 83, 337-391 (2001). MSC: 35P05 35B10 35P20 PDFBibTeX XMLCite \textit{M. Sh. Birman} and \textit{M. Solomyak}, J. Anal. Math. 83, 337--391 (2001; Zbl 1200.35196) Full Text: DOI
Birman, M. Sh.; Laptev, A.; Solomyak, M. On the eigenvalue behaviour for a class of differential operators on the semiaxis. (English) Zbl 0916.34067 Math. Nachr. 195, 17-46 (1998). Reviewer: Vjacheslav Yurko (Saratov) MSC: 34L15 34L20 PDFBibTeX XMLCite \textit{M. Sh. Birman} et al., Math. Nachr. 195, 17--46 (1998; Zbl 0916.34067) Full Text: DOI
Naimark, K.; Solomyak, M. Regular and pathological eigenvalue behavior for the equation \(-\lambda u''=Vu\) on the semiaxis. (English) Zbl 0895.34063 J. Funct. Anal. 151, No. 2, 504-530 (1997). Reviewer: T.Regińska (Warszawa) MSC: 34L20 PDFBibTeX XMLCite \textit{K. Naimark} and \textit{M. Solomyak}, J. Funct. Anal. 151, No. 2, 504--530 (1997; Zbl 0895.34063) Full Text: DOI
Levin, Daniel; Solomyak, Michael The Rozenblum-Lieb-Cwikel inequality for Markov generators. (English) Zbl 0910.47017 J. Anal. Math. 71, 173-193 (1997). Reviewer: M.Perelmuter (Kyïv) MSC: 47B25 PDFBibTeX XMLCite \textit{D. Levin} and \textit{M. Solomyak}, J. Anal. Math. 71, 173--193 (1997; Zbl 0910.47017) Full Text: DOI
Birman, Mikhail Sh.; Laptev, Ari; Solomyak, Michael The negative discrete spectrum of the operator \((-\Delta)^ l-\alpha V\) in \(L_ 2(\mathbb{R}^ d)\) for \(d\) even and \(2l\geq d\). (English) Zbl 0876.35079 Ark. Mat. 35, No. 1, 87-126 (1997). Reviewer: F.Mantlik (Dortmund) MSC: 35P20 35J10 PDFBibTeX XMLCite \textit{M. Sh. Birman} et al., Ark. Mat. 35, No. 1, 87--126 (1997; Zbl 0876.35079) Full Text: DOI
Birman, M.; Solomyak, M. Tensor product of a finite number of spectral measures is always a spectral measure. (English) Zbl 0844.47013 Integral Equations Oper. Theory 24, No. 2, 179-187 (1996). MSC: 47B15 47A80 28B15 PDFBibTeX XMLCite \textit{M. Birman} and \textit{M. Solomyak}, Integral Equations Oper. Theory 24, No. 2, 179--187 (1996; Zbl 0844.47013) Full Text: DOI
Newman, Joshua; Solomyak, Michael Two-sided estimates on singular values for a class of integral operators on the semi-axis. (English) Zbl 0817.47024 Integral Equations Oper. Theory 20, No. 3, 335-349 (1994). MSC: 47B10 47G10 47B38 47L20 45P05 34L15 PDFBibTeX XMLCite \textit{J. Newman} and \textit{M. Solomyak}, Integral Equations Oper. Theory 20, No. 3, 335--349 (1994; Zbl 0817.47024) Full Text: DOI
Olevskii, V.; Solomyak, M. An estimate for Schur multipliers in \(S_ p\)-classes. (English) Zbl 0806.15020 Linear Algebra Appl. 208-209, 57-64 (1994). Reviewer: K.H.Kim (Montgomery) MSC: 15A60 PDFBibTeX XMLCite \textit{V. Olevskii} and \textit{M. Solomyak}, Linear Algebra Appl. 208--209, 57--64 (1994; Zbl 0806.15020) Full Text: DOI
Solomyak, Michael A remark on the Hardy inequalities. (English) Zbl 0812.26007 Integral Equations Oper. Theory 19, No. 1, 120-124 (1994). Reviewer: B.Opic (Praha) MSC: 26D10 PDFBibTeX XMLCite \textit{M. Solomyak}, Integral Equations Oper. Theory 19, No. 1, 120--124 (1994; Zbl 0812.26007) Full Text: DOI
Solomyak, M. Piecewise-polynomial approximation of functions from \(H^ \ell((0,1)^ d)\), \(2\ell=d\), and applications to the spectral theory of the Schrödinger operator. (English) Zbl 0803.47045 Isr. J. Math. 86, No. 1-3, 253-275 (1994). MSC: 47F05 46E35 35J10 35P15 PDFBibTeX XMLCite \textit{M. Solomyak}, Isr. J. Math. 86, No. 1--3, 253--275 (1994; Zbl 0803.47045) Full Text: DOI
Birman, M. Sh.; Solomyak, M. Z. Construction in a piecewise smooth domain of a function of the class \(H^ 2\) from the value of the conormal derivative. (English. Russian original) Zbl 0696.46039 J. Sov. Math. 49, No. 5, 1128-1136 (1990). MSC: 46J15 PDFBibTeX XMLCite \textit{M. Sh. Birman} and \textit{M. Z. Solomyak}, J. Sov. Math. 49, No. 5, 1128--1136 (1990; Zbl 0696.46039) Full Text: DOI
Birman, M. Sh.; Solomyak, M. Z. Estimates for the difference of fractional powers of selfadjoint operators in the case of unbounded perturbations. (English. Russian original) Zbl 0784.47011 J. Sov. Math. 61, No. 2, 2018-2035 (1992); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 178, 120-145 (1989). MSC: 47A30 47A60 47B47 47B25 PDFBibTeX XMLCite \textit{M. Sh. Birman} and \textit{M. Z. Solomyak}, J. Sov. Math. 61, No. 2, 1 (1989; Zbl 0784.47011); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 178, 120--145 (1989) Full Text: DOI
Birman, M. Sh.; Solomyak, M. Z. Operator integration, perturbations, and commutators. (English. Russian original) Zbl 0784.47033 J. Sov. Math. 63, No. 2, 129-148 (1993); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 170, 34-66 (1989). MSC: 47B06 47B15 47B47 PDFBibTeX XMLCite \textit{M. Sh. Birman} and \textit{M. Z. Solomyak}, J. Sov. Math. 63, No. 2, 1 (1989; Zbl 0784.47033); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 170, 34--66 (1989) Full Text: DOI
Birman, M. Sh.; Solomyak, M. Z. Asymptotic behavior of the spectrum of variational problems on the solutions of elliptic systems. (English) Zbl 0562.35064 J. Sov. Math. 28, 633-644 (1985). MSC: 35P20 35J45 49R50 PDFBibTeX XMLCite \textit{M. Sh. Birman} and \textit{M. Z. Solomyak}, J. Sov. Math. 28, 633--644 (1985; Zbl 0562.35064) Full Text: DOI
Birman, M. Sh.; Solomyak, M. Z. Compact operators whose singular numbers have powerlike asymptotics. (English) Zbl 0546.47010 J. Sov. Math. 27, 2442-2447 (1984). MSC: 47B10 35P20 PDFBibTeX XMLCite \textit{M. Sh. Birman} and \textit{M. Z. Solomyak}, J. Sov. Math. 27, 2442--2447 (1984; Zbl 0546.47010) Full Text: DOI
Karol’, A. I.; Solomyak, M. Z. Class of differential operators with abnormal behavior of the spectrum of the Dirichlet problem. (English) Zbl 0515.35066 Math. Notes 31, 379-381 (1982). MSC: 35P20 35J30 47B25 47F05 PDFBibTeX XMLCite \textit{A. I. Karol'} and \textit{M. Z. Solomyak}, Math. Notes 31, 379--381 (1982; Zbl 0515.35066) Full Text: DOI
Birman, M. Sh.; Solomyak, M. Z. Asymptotics of the spectrum of variational problems on solutions of elliptic equations in unbounded domains. (English. Russian original) Zbl 0463.35061 Funct. Anal. Appl. 14, 267-274 (1981); translation from Funkts. Anal. Prilozh. 14, No. 4, 27-35 (1980). MSC: 35P20 35R20 47F05 35J20 PDFBibTeX XMLCite \textit{M. Sh. Birman} and \textit{M. Z. Solomyak}, Funct. Anal. Appl. 14, 267--274 (1981; Zbl 0463.35061); translation from Funkts. Anal. Prilozh. 14, No. 4, 27--35 (1980) Full Text: DOI
Birman, M. Sh.; Solomyak, M. Z. Asymptotics of the spectrum of variational problems on solutions of elliptic equations. (English) Zbl 0427.35050 Sib. Math. J. 20, 1-15 (1979). MSC: 35P20 47F05 35J35 49R50 35S15 PDFBibTeX XMLCite \textit{M. Sh. Birman} and \textit{M. Z. Solomyak}, Sib. Math. J. 20, 1--15 (1979; Zbl 0427.35050) Full Text: DOI EuDML
Birman, M. Sh.; Solomyak, M. Z. Asymptotic behavior of the spectrum of differential equations. (English) Zbl 0424.35069 J. Sov. Math. 12, 247-283 (1979). MSC: 35P20 47F05 PDFBibTeX XMLCite \textit{M. Sh. Birman} and \textit{M. Z. Solomyak}, J. Sov. Math. 12, 247--283 (1979; Zbl 0424.35069) Full Text: DOI
Birman, M. Sh.; Solomyak, M. Z. Remarks on the spectral shift function. (English) Zbl 0336.47017 J. Sov. Math. 3, 408-419 (1975). MSC: 47B10 47A55 47B15 PDFBibTeX XMLCite \textit{M. Sh. Birman} and \textit{M. Z. Solomyak}, J. Sov. Math. 3, 408--419 (1975; Zbl 0336.47017) Full Text: DOI
Birman, M. Sh.; Solomyak, M. Z. Leading term in the asymptotic spectral formula for ”nonsmooth” elliptic problems. (English. Russian original) Zbl 0225.35077 Funct. Anal. Appl. 4, 265-275 (1970); translation from Funkts. Anal. Prilozh. 4, No. 4, 1-13 (1970). MSC: 35P20 PDFBibTeX XMLCite \textit{M. Sh. Birman} and \textit{M. Z. Solomyak}, Funct. Anal. Appl. 4, 265--275 (1970; Zbl 0225.35077); translation from Funkts. Anal. Prilozh. 4, No. 4, 1--13 (1970) Full Text: DOI