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JOURNALS // Algebra i Analiz

Algebra i Analiz, 2018, Volume 30, Issue 3, Pages 30–54 (Mi aa1593)

A general trace formula for the differential operator on a segment with the last coefficient perturbed by a finite signed measure
E. D. Gal'kovskiĭ, A. I. Nazarov

References

1. Vinokurov V. A., Sadovnichii V. A., “Asimptotika sobstvennykh znachenii i sobstvennykh funktsii i formula sleda dlya potentsiala, soderzhaschego $\delta$-funktsii”, Differents. uravneniya, 38:6 (2002), 735–751  mathnet  mathscinet  zmath
2. Gelfand I. M., Levitan B. M., “Ob odnom prostom tozhdestve dlya sobstvennykh znachenii differentsialnogo operatora vtorogo poryadka”, Dokl. AN SSSR, 88:4 (1953), 593–596  zmath
3. Konechnaya N. N., Safonova T. A., Tagirova R. N., “Asimptotika sobstvennykh znachenii i regulyarizovannyi sled pervogo poryadka operatora Shturma–Liuvillya s $\delta$-potentsialom”, Vestn. SAFU, 2016, no. 1, 104–113  mathscinet
4. Naimark M. A., Lineinye differentsialnye operatory, 2-e izd., Nauka, M., 1969  mathscinet
5. Nazarov A. I., “Exact $L_2$-small ball asymptotics of Gaussian processes and the spectrum of boundary-value problems”, J. Theoret. Probab., 22:3 (2009), 640–665  crossref  mathscinet  zmath  elib
6. Nazarov A. I., Stolyarov D. M., Zatitskiy P. B., “The Tamarkin equiconvergence theorem and a first-order trace formula for regular differential operators revisited”, J. Spectr. Theory, 4:2 (2014), 365–389  crossref  mathscinet  zmath  elib
7. Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady. Elementarnye funktsii, Nauka, M., 1981  mathscinet
8. Savchuk A. M., “Regulyarizovannyi sled pervogo poryadka operatora Shturma–Liuvillya s $\delta$-potentsialom”, Uspekhi mat. nauk, 55:6 (2000), 155–156  mathnet  crossref  mathscinet  zmath
9. Savchuk A. M., Shkalikov A. A., “Formula sleda dlya operatorov Shturma–Liuvillya s singulyarnymi potentsialami”, Mat. zametki, 69:3 (2001), 427–442  mathnet  crossref  mathscinet  zmath
10. Sadovnichii V. A., Podolskii V. E., “Sledy operatorov”, Uspekhi mat. nauk, 61:5 (2006), 89–156  mathnet  crossref  mathscinet  zmath  elib
11. Tamarkin Ya. D., O nekotorykh obschikh zadachakh teorii obyknovennykh differentsialnykh uravnenii i o razlozhenii proizvolnykh funktsii v ryady, Petrograd, 1917
12. Shkalikov A. A., “Kraevye zadachi dlya obyknovennykh differentsialnykh uravnenii s parametrom v granichnykh usloviyakh”, Tr. semin. im. I. G. Petrovskogo, 9, 1983, 140–179
13. Shevchenko R. F., “O slede differentsialnogo operatora”, Dokl. AN SSSR, 164:1 (1965), 62–65  mathnet  mathscinet  zmath


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