Related papers: Potential theory with multivariate kernels
For arbitrary nontrivial linear combinations of a finite number of Poisson kernels, the fulfillment of the Nagy condition is established for all numbers n, starting from some number. It is also proved for any n the existence of linear…
We consider volume-constrained minimizers of the fractional perimeter with the addition of a potential energy in the form of a volume inte- gral. Such minimizers are solutions of the prescribed fractional curvature problem. We prove…
This paper is concerned with volume-constrained minimization problems derived from Gamow's liquid drop model for the atomic nucleus, involving the competition of a perimeter term and repulsive nonlocal potentials. We consider a large class…
We review origins and developments of Noncommutative Potential theory as underpinned by the notion of energy form. Recent and new applications are shown to approximation properties of von Neumann algebras.
Kernelization---a mathematical key concept for provably effective polynomial-time preprocessing of NP-hard problems---plays a central role in parameterized complexity and has triggered an extensive line of research. This is in part due to a…
Our main result shows that if a lower-semicontinuous kernel K satisfies some mild additional hypotheses, then asympotitically polarization optimal configurations are precisely those that are asymptotically distributed according to the…
The possibility of a modification of special relativity with an invariant energy scale playing the role of a minimum energy is explored. Consistency with the equivalence of different inertial frames is obtained by an appropriate choice of a…
We prove existence and uniqueness of a solution to the problem of minimizing the logarithmic energy of vector potentials associated to a $d$-tuple of positive measures supported on closed subsets of the complex plane. The assumptions we…
We propose a formal resource theoretic approach to asses the coherence between partially polarized electromagnetic fields. We show that naturally defined incoherent operations endow partial coherence with a preorder relation that must be…
The present work develops certain analytical tools required to construct and compute invariant kernels on the space of complex covariance matrices. The main result is the $\mathrm{L}^1$--Godement theorem, which states that any invariant…
We calculate the energy of the state closest to threshold for two and three identical, spinless particles confined to a cubic spatial volume with periodic boundary conditions and with zero total momentum in the finite-volume frame. The…
We consider a constrained minimal energy problem with an external field over noncompact classes of infinite dimensional vector measures on a locally compact space. The components are positive measures (charges) that are constrained from…
In the context of kernel optimization, we prove a result that yields new factorizations and realizations. Our initial context is that of general positive operator-valued kernels. We further present implications for Hilbert space-valued…
The Many Worlds Interpretation (MWI) famously avoids the issue of wave function collapse. Different MWI trees representing the same quantum events can have different topologies, depending upon the observer. However, they are all isomorphic…
We discuss the dynamics of a charged nonrelativistic particle in electromagnetic field of a rotating magnetized celestial body. The equations of motion of the particle are obtained and some particular solutions are found. Effective…
In the framework of idempotent mathematics, analogs of the classical kernel theorems of L. Schwartz and A. Grothendieck are studied. Idempotent versions of nuclear spaces (in the sense of A. Grothendieck) are discussed. The so-called…
A model for low-energy meson-baryon interaction in the strange sector is presented. The interaction is described in terms of separable potentials with multiple partial waves considered. A general solution of Lippmann-Schwinger equation for…
The Lorentz-violating model proposed by Myers and Pospelov suffers from a higher-derivative pathology due to a dimension-5 operator. In particular, its electromagnetic sector exhibits an spectrum which contains, in addition to an expected…
With regard to generic two-component systems, the theory of first variations of global quantities is reviewed and explicit expressions are inferred for subsystem potential energies and potential-energy tensors. Performing a conceptual…
In quantum field theory the concept of a Lagrangian interaction density, expressed in terms of fields, is primary. Forces between two particles are regarded as arising primarily from the exchange of quanta of the bosonic fields. Thus, in…