| Title:
|
A singular spectral identity and inequality involving the Dirichlet integral of an ordinary differential expression (English) |
| Author:
|
Everitt, William Norrie |
| Author:
|
Wray, S. D. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
32 |
| Issue:
|
4 |
| Year:
|
1982 |
| Pages:
|
589-607 |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| MSC:
|
34B25 |
| MSC:
|
47E05 |
| idZBL:
|
Zbl 0533.34026 |
| idMR:
|
MR682134 |
| DOI:
|
10.21136/CMJ.1982.101836 |
| . |
| Date available:
|
2008-06-09T14:50:42Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/101836 |
| . |
| Reference:
|
[1] Amos R. J., Everitt W. N.: On a quadratic integral inequality.Proc. Roy. Soc. Edinburgh Sect. A 78 (1978), 241-256. Zbl 0393.26008, MR 0466454 |
| Reference:
|
[2] Amos R. J., Everitt W. N.: On integral inequalities and compact embeddings associated with ordinary differential expressions.Arch. Rational Mech. Anal. 71 (1979), 15-40. Zbl 0427.26007, MR 0522705, 10.1007/BF00250668 |
| Reference:
|
[3] Bradley J. S., Everitt W. N.: Inequalities associated with regular and singular problems in the calculus of variations.Trans. Amer. Math. Soc. 182 (1973), 303 - 321. Zbl 0273.26010, MR 0330606, 10.1090/S0002-9947-1973-0330606-8 |
| Reference:
|
[4] Bradley J. S., Everitt W. N.: A singular integral inequality on a bounded interval.Proc. Amer. Math. Soc. 61 (1976), 29-35. MR 0425249, 10.1090/S0002-9939-1976-0425249-X |
| Reference:
|
[5] Evans W. D.: On limit-point and Dirichlet-type results for second-order differential expressions.Lecture Notes in Mathematics 564, Springer, Berlin (1976). Zbl 0388.34013, MR 0593161, 10.1007/BFb0087329 |
| Reference:
|
[6] Everitt W. N., Hinton D. B., Wong J. S. W.: On the strong limit - $n$ classification of linear ordinary differential expressions of order 2$n$.Proc. London Math. Soc. 29 (1974), 351-367. MR 0409956 |
| Reference:
|
[7] Everitt W. N.: On the strong limit-point condition of second-order differential expressions.International conference on differential equations, 287-307, Academic Press, New York (1975). Zbl 0339.34018, MR 0435497 |
| Reference:
|
[8] Everitt W. N.: A note on the Dirichlet condition for second-order differential expressions.Canad. J. Math. XXVIII (1976), 312-320. Zbl 0338.34011, MR 0430391, 10.4153/CJM-1976-033-3 |
| Reference:
|
[9] Friedrichs K. О.: Spektraltheorie halbbeschränkter Operatoren und Anwendung auf die Spektralzerlegung von Differentialoperatoren, I.Math. Ann. 109 (1934), 465 - 487. Zbl 0008.39203, MR 1512905, 10.1007/BF01449150 |
| Reference:
|
[10] Friedrichs K. O.: Spectral theory of operators in Hilbert space.Springer, Berlin (1973). Zbl 0266.47001, MR 0470698 |
| Reference:
|
[11] Hinton D. В.: On the eigenfunction expansions of singular ordinary differential equations.J. Differential Equations 24 (1977), 282-308. Zbl 0405.34025, MR 0454140, 10.1016/0022-0396(77)90152-8 |
| Reference:
|
[12] Hinton D. В.: Eigenfunction expansions and spectral matrices of singular differential operators.Proc. Roy. Soc. Edinburgh Sect. A 80 (1978), 289-308. Zbl 0389.34021, MR 0516229 |
| Reference:
|
[13] Kolf H.: Remarks on some Dirichlet type results for semibounded Sturm-Liouville operators.Math. Ann. 210 (1974), 197-205. MR 0355177, 10.1007/BF01350583 |
| Reference:
|
[14] Kato T.: Perturbation theory for linear operators.(1st Edn.), Springer, Berlin (1966). Zbl 0148.12601 |
| Reference:
|
[15] Kwong M. K.: Note on the strong limit point condition of second order differential expressions.Quart. J. Math. Oxford (2), 28 (1977), 201-208. Zbl 0403.34025, MR 0450658, 10.1093/qmath/28.2.201 |
| Reference:
|
[16] Kwong M. K.: Conditional Dirichlet property of second order differential expressions.Quart. J. Math. Oxford (2) 28 (1977), 329-338. Zbl 0425.34002, MR 0454128, 10.1093/qmath/28.3.329 |
| Reference:
|
[17] Naĭmark M. A.: Linear differential operators: II.Ungar, New York (1968). |
| Reference:
|
[18] Putnam C. R.: An application of spectral theory to a singular calculus of variations problem.Amer. J. Math. 70 (1948), 780-803. Zbl 0038.26501, MR 0030133, 10.2307/2372212 |
| Reference:
|
[19] Sears D. B., Wray S. D.: An inequality of C. R. Putnam involving a Dirichlet functional.Proc. Roy. Soc. Edinburgh Sect. A 75 (1976), 199-207. Zbl 0334.34024, MR 0445057 |
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