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Resolvent and Scattering Matrix at the Maximum of the Potential

Alexandrova, Ivana, Bony, Jean-François, Ramond, Thierry (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 35P25, 81U20, 35S30, 47A10, 35B38.We study the microlocal structure of the resolvent of the semiclassical Schrödinger operator with short range potential at an energy which is a unique non-degenerate global maximum of the potential. We prove that it is a semiclassical Fourier integral operator quantizing the incoming and outgoing Lagrangian submanifolds associated to the fixed hyperbolic point. We then discuss two applications of this result to describing...

Resolvent and spectrum of a nonselfadjoint differential operator in a Hilbert space

Michael Gil (2012)

Annales UMCS, Mathematica

We consider a second order regular differential operator whose coefficients are nonselfadjoint bounded operators acting in a Hilbert space. An estimate for the resolvent and a bound for the spectrum are established. An operator is said to be stable if its spectrum lies in the right half-plane. By the obtained bounds, stability and instability conditions are established.

Resolvent conditions and powers of operators

Olavi Nevanlinna (2001)

Studia Mathematica

We discuss the relation between the growth of the resolvent near the unit circle and bounds for the powers of the operator. Resolvent conditions like those of Ritt and Kreiss are combined with growth conditions measuring the resolvent as a meromorphic function.

Restriction of an operator to the range of its powers

M. Berkani (2000)

Studia Mathematica

Let T be a bounded linear operator acting on a Banach space X. For each integer n, define T n to be the restriction of T to R ( T n ) viewed as a map from R ( T n ) into R ( T n ) . In [1] and [2] we have characterized operators T such that for a given integer n, the operator T n is a Fredholm or a semi-Fredholm operator. We continue those investigations and we study the cases where T n belongs to a given regularity in the sense defined by Kordula and Müller in[10]. We also consider the regularity of operators with topological...

Revisiting the construction of gap functions for variational inequalities and equilibrium problems via conjugate duality

Liana Cioban, Ernö Csetnek (2013)

Open Mathematics

Based on conjugate duality we construct several gap functions for general variational inequalities and equilibrium problems, in the formulation of which a so-called perturbation function is used. These functions are written with the help of the Fenchel-Moreau conjugate of the functions involved. In case we are working in the convex setting and a regularity condition is fulfilled, these functions become gap functions. The techniques used are the ones considered in [Altangerel L., Boţ R.I., Wanka...

Rings of PDE-preserving operators on nuclearly entire functions

Henrik Petersson (2004)

Studia Mathematica

Let E,F be Banach spaces where F = E’ or vice versa. If F has the approximation property, then the space of nuclearly entire functions of bounded type, ℋ N b ( E ) , and the space of exponential type functions, Exp(F), form a dual pair. The set of convolution operators on ℋ N b ( E ) (i.e. the continuous operators that commute with all translations) is formed by the transposes φ ( D ) ≡ t φ , φ ∈ Exp(F), of the multiplication operators φ :ψ ↦ φ ψ on Exp(F). A continuous operator T on ℋ N b ( E ) is PDE-preserving for a set ℙ ⊆ Exp(F) if it...

Currently displaying 81 – 100 of 103