In this work we analyse the solution to the recurrence equation M_Ψ(z+1)=-zΨ(-
z)M_Ψ(z),\quadM_Ψ(1)=1, defined on a subset of the imaginary line and where -Ψ is any …

This textbook introduces the study of partial differential equations using both analytical and
numerical methods. By intertwining the two complementary approaches, the authors create …

Shape optimization conjectures for the first two eigenvalues of the Robin Laplacian are
developed and supported with new results for rectangular boxes. The square minimizes the …

In this paper, we start by showing that the intertwining relationship between two minimal
Markov semigroups acting on Hilbert spaces implies that any recurrent extensions, in the …

Numerous processes in nature, medicine, economics, and technology can be described by
partial differential equations (PDEs). This alone is enough to explain the enormous interest …

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This dissertation consists of three parts. In the first part, we establish a spectral theory in the
Hilbert space L 2 (R+) of the C 0-semigroup P and its adjoint Pˆ having as generator …

The most commonly considered counterexamples to Kac's famous question “can one hear
the shape of a drum?”–ie, does isospectrality of two Laplacians on domains imply that the …

The available frequencies that make up the sound of our system are the eigenvalues of the
Laplacian. Furthermore, the concentration of energy can also be expressed in the form of …

Theory of Exponential Functionals of Lévy Processes Page 1 Theory of Exponential Functionals
of Lévy Processes Mladen S. Savov Institute of Mathematics and Informatics Bulgarian …