On norm of single layer potentials on segments
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Seyed M. Zoalroshd
Abstract
We show that, for a special case, equality of the spectra of single layer potentials defined on two segments implies that these segments must have equal length. We also provide an upper bound for the operator norm and exact expression for the Hilbert–Schmidt norm of single layer potentials on segments.
The author would like to express his sincere appreciation to his advisor, Professor Dmitry Khavinson, for his comments and suggestions regarding this paper. The author also would like to thank the anonymous reviewer for his/her suggestions and comments.
References
1 G. B. Folland, Introduction to Partial Differential Equations, Princeton University Press, Princeton, 1995. Search in Google Scholar
2 M. Kac, Can one hear the shape of a drum?, Amer. Math. Monthly 73 (1966), 1–23. 10.1080/00029890.1966.11970915Search in Google Scholar
3 R. Kress, V. Maz'ya and V. Kozlov, Linear Integral Equations, Springer, Berlin, 1989. 10.1007/978-3-642-97146-4Search in Google Scholar
4 N. I. Muskhelishvili, Singular Integral Equations. Boundary Problems of Functions Theory and Their Application to Mathematical Physics, P. Noordhoff, Groningen, 1953. Search in Google Scholar
5 A. Pietsch, Eigenvalues and s-Numbers, Cambridge Stud. Adv. Math. 13, Cambridge University Press, Cambridge, 1987. Search in Google Scholar
6 K. Zhu, Operator Theory in Function Spaces 138, American Mathematical Society, Providence, 2007. 10.1090/surv/138Search in Google Scholar
© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Admissible pair of spaces for non-correctly solvable linear differential equations
- Defective functions of meromorphic functions in the unit disc
- A boundary-value problem for the equation of mixed type with generalized operators of fractional differentiation in the boundary conditions
- Density not realizable as the Jacobian determinant of a bilipschitz map
- An inequality involving the gamma and digamma functions
- Asymptotic behaviour of solutions to one-dimensional reaction diffusion cooperative systems involving infinitesimal generators
- Generalized slow growth of special monogenic functions
- Iterative algorithm for the split equality problem in Hilbert spaces
- On norm of single layer potentials on segments
Articles in the same Issue
- Frontmatter
- Admissible pair of spaces for non-correctly solvable linear differential equations
- Defective functions of meromorphic functions in the unit disc
- A boundary-value problem for the equation of mixed type with generalized operators of fractional differentiation in the boundary conditions
- Density not realizable as the Jacobian determinant of a bilipschitz map
- An inequality involving the gamma and digamma functions
- Asymptotic behaviour of solutions to one-dimensional reaction diffusion cooperative systems involving infinitesimal generators
- Generalized slow growth of special monogenic functions
- Iterative algorithm for the split equality problem in Hilbert spaces
- On norm of single layer potentials on segments
