Results 11 to 20 of about 596 (38)

On the spectra of non‐selfadjoint differential operators and their adjoints in direct sum spaces

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 9, Page 557-574, 2003., 2003
The general ordinary quasidifferential expression Mp of nth order, with complex coefficients and its formal adjoint Mp+ on any finite number of intervals Ip = (ap, bp), p = 1, …, N, are considered in the setting of the direct sums of Lwp2(ap,bp)‐spaces of functions defined on each of the separate intervals.
Sobhy El-Sayed Ibrahim
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On the domain of selfadjoint extension of the product of Sturm‐Liouville differential operators

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 11, Page 695-709, 2003., 2003
The second‐order symmetric Sturm‐Liouville differential expressions τ1, τ2, …, τn with real coefficients are considered on the interval I = (a, b), −∞ ≤ a < b ≤ ∞. It is shown that the characterization of singular selfadjoint boundary conditions involves the sesquilinear form associated with the product of Sturm‐Liouville differential expressions and ...
Sobhy El-Sayed Ibrahim
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Remarks on embeddable semigroups in groups and a generalization of some Cuthbert′s results

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 22, Page 1421-1431, 2003., 2003
Let (U(t)) t≥0 be a C0‐semigroup of bounded linear operators on a Banach space X. In this paper, we establish that if, for some t0 > 0, U(t0) is a Fredholm (resp., semi‐Fredholm) operator, then (U(t)) t≥0 is a Fredholm (resp., semi‐Fredholm) semigroup.
Khalid Latrach, Abdelkader Dehici
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A spectral mapping theorem for semigroups solving PDEs with nonautonomous past

Abstract and Applied Analysis, Volume 2003, Issue 16, Page 933-951, 2003., 2003
We prove a spectral mapping theorem for semigroups solving partial differential equations with nonautonomous past. This theorem is then used to give spectral conditions for the stability of the solutions of the equations.
Genni Fragnelli
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Kreĭn′s trace formula and the spectral shift function

International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 4, Page 239-252, 2001., 2001
Let A, B be two selfadjoint operators whose difference B − A is trace class. Kreĭn proved the existence of a certain function ξ ∈ L1(ℝ) such that tr[f(B) − f(A)] = ∫ℝf′(x)ξ(x)dx for a large set of functions f. We give here a new proof of this result and discuss the class of admissible functions.
Khristo N. Boyadzhiev
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Evolution semigroups for nonautonomous Cauchy problems

Abstract and Applied Analysis, Volume 2, Issue 1-2, Page 73-95, 1997., 1997
In this paper, we characterize wellposedness of nonautonomous, linear Cauchy problems on a Banach space X by the existence of certain evolution semigroups. Then, we use these generation results for evolution semigroups to derive wellposedness for nonautonomous Cauchy problems under some “concrete” conditions.
Gregor Nickel
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Iterative solution of unstable variational inequalities on approximately given sets

Abstract and Applied Analysis, Volume 1, Issue 1, Page 45-64, 1996., 1996
The convergence and the stability of the iterative regularization method for solving variational inequalities with bounded nonsmooth properly monotone (i.e., degenerate) operators in Banach spaces are studied. All the items of the inequality (i.e., the operator A, the “right hand side” f and the set of constraints Ω) are to be perturbed. The connection
Y. I. Alber, A. G. Kartsatos, E. Litsyn
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Bifurcation for the solutions of equations involving set valued mappings

International Journal of Mathematics and Mathematical Sciences, Volume 8, Issue 1, Page 37-48, 1985., 1985
This paper is devoted to a generalization of the bifurcation theorem of Karsnosel′skii and Rabinowitz to the set valued situation.
E. U. Tarafdar, H. B. Thompson
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A theorem on “localized” self‐adjointness of Shrödinger operators with ‐potentials

International Journal of Mathematics and Mathematical Sciences, Volume 5, Issue 3, Page 545-552, 1982., 1982
We prove a result which concludes the self‐adjointness of a Schrödinger operator from the self‐adjointness of the associated “localized” Schrödinger operators having ‐Potentials.
Hans L. Cycon
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Absolute continuity and hyponormal operators

International Journal of Mathematics and Mathematical Sciences, Volume 4, Issue 2, Page 321-335, 1981., 1981
Let T be a completely hyponormal operator, with the rectangular representation T = A + iB, on a separable Hilbert space. If 0 is not an eigenvalue of T* then T also has a polar factorization T = UP, with U unitary. It is known that A, B and U are all absolutely continuous operators.
C. R. Putnam
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