David Krejcirik's page: 
EXPRO grant project
New challenges for spectral theory:

The ultimate goal of the project is to develop unconventional tools in spectral theory in order to tackle various newly born, or more classical but recently revived, open problems in mathematics and physics. Among the variety of problems, I intend to particularly consider hot open questions in: spectral geometry of optimal shapes and eigenfunction properties; mathematical models of modern nanostructures, graphene and metamaterials; new concepts in quantum mechanics with nonselfadjoint operators, Schrödinger and Dirac operators with complex potentials, damped wave systems, nonstandard stochastic processes and asymptotic distribution of eigenvalues of structured matrices. These apparently unrelated problems are in fact interlinked and a crossfertilisation of ideas and techniques will constitute an important part of the project. As examples of the synergy, I propose to develop the method of multipliers to become a standard tool in spectral theory of differential operators with complex coefficients and explain the cloaking effect in metamaterials by operatortheoretic methods. 
Vibrating circular membrane with attractive boundary conditions 
researchers  doctoral students  undergraduate students 



T. Vu:
Spectral inequality for Dirac right triangles; J. Math. Phys. 64 (2023) 041502. 
W. Borrelli, Ph. Briet, D. Krejcirik and T. OurmieresBonafos:
Spectral properties of relativistic quantum waveguides; Ann. Henri Poincare 23 (2022) 40694114. 
Ph. Briet and D. Krejcirik:
Spectral optimisation of Dirac rectangles; J. Math. Phys. 63 (2022) 013502. 
S. Kondej, D. Krejcirik and J. Kriz:
Soft quantum waveguides with an explicit cutlocus; J. Phys. A: Math. Theor. 54 (2021) 30LT01. 
M. Tichy:
The asymptotic behaviour of the heat equation in a sheared unbounded strip; J. Differential Equations 297 (2021) 575600. 
D. Krejcirik, V. Lotoreichik, K. Pankrashkin and M. Tusek:
Spectral analysis of the multidimensional diffusion operator with random jumps from the boundary; J. Evol. Equ. 21 (2021) 16511675. 
T. G. Pedersen, H. Cornean, D. Krejcirik, N. Raymond and E. Stockmeyer:
Starklocalization as a probe of nanostructure geometry; New. J. Phys 24 (2022) 093005. 
H. Cornean, D. Krejcirik, T. G. Pedersen, N. Raymond and E. Stockmeyer:
On the twodimensional quantum confined Stark effect in strong electric fields; SIAM J. Math. Anal. 54 (2022) 21142127. 
D. Krejcirik and P. Antunes:
Bound states in semiDirac semimetals; Phys. Lett. A 386 (2021) 126991. 
T. Kalvoda and F. Stampach:
New family of symmetric orthogonal polynomials and a solvable model of a kinetic spin chain; J. Math. Phys. 61 (2020) 103305. 
T. Nguyen Duc:
Pseudomodes for biharmonic operators with complex potentials; SIAM J. Math. Anal. 55 (2023) 65806624 
M. C. Camara and D. Krejcirik:
Complexselfadjointness; Anal. Math. Phys. 13 (2023) art. no. 6. 
I. Semorádová and P. Siegl:
Diverging Eigenvalues in Domain Truncations of Schrödinger Operators with Complex Potentials; SIAM J. Math. Anal. 54 (2022) 50645101. 
N.A. Lai and N.M. Schiavone:
Blowup and lifespan estimate for generalized Tricomi equations related to Glassey conjecture; Math. Z. 301 (2022) 33693393. 
H. Mizutani and N. M. Schiavone:
Spectral enclosures for Dirac operators perturbed by rigid potentials; Rev. Math. Phys. 34 (2022) 2250023. 
L. Heriban and M. Tusek:
Nonselfadjoint relativistic point interaction in one dimension; J. Math. Anal. Appl. 516 (2022) 126536. 
D. Krejcirik, A. Laptev and F. Stampach:
Spectral enclosures and stability for nonselfadjoint discrete Schrodinger operators on the halfline; Bull. London. Math. Soc. 54 (2022) 23792403. 
M. Hansmann and D. Krejcirik:
The abstract BirmanSchwinger principle and spectral stability; J. Anal. Math. 148 (2022) 361398. 
D. Krejcirik and T. Nguyen Duc:
Pseudomodes for nonselfadjoint Dirac operators; J. Funct. Anal. 282 (2022) 109440. 
D. Krejcirik and F. Stampach:
A sharp form of the discrete Hardy inequality and the KellerPinchoverPogorzelski inequality; Amer. Math. Monthly 129 (2022) 281283. 
F. Stampach and P. Stovicek:
On diagonalizable quantum weighted Hankel matrices; chapter to the book series Toeplitz Operators and Random Matrices: In Memory of Harold Widom, Operator Theory: Advances and Applications, 289, Birkhäuser, 2022. 
F. Stampach:
Asymptotic spectral properties of the Hilbert Lmatrix; SIAM J. Matrix Anal. Appl. 43 (2022) 16581679. 
F. Stampach:
The Hilbert Lmatrix; J. Funct. Anal. 282 (2022) 146. 
P. D'Ancona, L. Fanelli, D. Krejcirik, N. M. Schiavone:
Localization of eigenvalues for nonselfadjoint Dirac and KleinGordon operators; Nonlinear Anal. 214 (2022) 112565. 
D. Kramar:
The collapse of quasiselfadjointness at the exceptional points of a PTsymmetric model with complex Robin boundary conditions; J. Phys. A: Math. Theor. 54 (2021) 415202. 
S. Bogli and F. Stampach:
On LiebThirring inequalities for onedimensional nonselfadjoint Jacobi and Schrödinger operators; J. Spectr. Theory 11 (2021), 13911413.2 
O. O. Ibrogimov, D. Krejcirik and A. Laptev:
Sharp bounds for eigenvalues of biharmonic operators with complex potentials in low dimensions; Math. Nachr. 294 (2021) 13331349. 
P. Blaschke and F. Stampach:
The asymptotic zero distribution of Lommel polynomials as polynomials of their order with a variable complex argument; J. Math. Anal. Appl. 490 (2020) 124238. 
D. Krejcirik and T. Kurimaiova:
From LiebThirring inequalities to spectral enclosures for the damped wave equation; Integral Equations Operator Theory 92 (2020) 47. 
37 Jun 2024 
CIRM conference:
Mathematical aspects of the physics with nonselfadjoint operators; Marseille, France. 
1015 Jul 2022 
BIRS workshop:
Mathematical aspects of the physics with nonselfadjoint operators; Banff, Canada. 
15 Feb 2021

CIRM conference:
Mathematical aspects of the physics with nonselfadjoint operators: 10 years after; Marseille, France. 
Last modified: 9 November 2023 