125 papers
This paper extends diffraction tomography to accommodate focused beam scanning by modeling incident fields as Herglotz waves, deriving a new Fourier diffraction relation that enables quantitative reconstruction and reveals how different scan geometries impact the imaging results.
This paper establishes that in raster scan diffraction tomography using focused beams, the object's scattering potential is generically uniquely determined in dimensions higher than two, whereas in two dimensions, only a specific subset of Fourier coefficients can be uniquely recovered while others remain ambiguous.
This paper provides a complete classification of when two continuous wavelet systems associated with matrix groups in two dimensions generate identical scales of coorbit spaces, thereby offering a rigorous framework for comparing their approximation-theoretic properties.
This paper establishes new weighted Sobolev embedding theorems and a Pólya-Szegö type inequality derived from an isoperimetric problem to analyze a class of semilinear degenerate elliptic equations in a three-dimensional domain, thereby extending existing results to higher dimensions.
This paper introduces a model-agnostic framework that improves function extrapolation by projecting baseline approximations onto feasible sets defined by anchor functions, thereby providing rigorous, proven bounds that guarantee error reduction in extrapolation regions.
This paper revisits Kippenhahn's conjecture regarding the unitary equivalence of Hermitian matrix pairs with repeated characteristic polynomial factors by employing local spectral analysis to establish necessary and sufficient conditions for the conjecture's validity.
This paper introduces a flexible transformed minimization model with two adjustable parameters to enhance sparse signal recovery, establishing exact and stable recovery guarantees via the restricted isometry property, proposing an efficient IRLSTLp algorithm with convergence proofs, and demonstrating its superior performance and theoretical bounds through numerical experiments.
This paper resolves the open case for in Pelczyński's theorem by constructing -injective but not -injective Banach spaces via an iterative "zero-sum" subspace technique, while also establishing a new upper bound of $9+6\sqrt{3}L_\infty[0,1]\ell_\infty$.
This paper revisits and expands the theory of Dunford-Pettis multilinear operators by introducing new classes, establishing their relationships with existing and emerging operator ideals, and analyzing inclusion and coincidence conditions.
This paper establishes convex body domination results for generalized vector-valued commutators of operators that already admit such domination, deriving strong type estimates and characterizing the associated BMO spaces.
This paper establishes uniform concentration inequalities for random matrices with -subexponential tails (), extending optimal subgaussian results to heavier-tailed distributions and providing new guarantees for robust high-dimensional inference and dimension reduction.
This paper establishes a pointwise geometric description of nonlinear Lebesgue spaces, including their length structure, curvature bounds, and speed definitions for absolutely continuous curves, by first proving a nonlinear Fubini–Lebesgue theorem that identifies L^p curves with mappings into the space of L^p curves.
This paper establishes a new boundedness criterion for the maximal operator on variable Lebesgue spaces, formulated in terms of a variable exponent analogue of the weighted condition.
This paper provides a rigorous counterexample demonstrating that the property of all derivations from a Banach algebra into a dense ideal being inner does not imply that all derivations into the algebra itself are inner, specifically using the algebra of compact operators and its dense ideal of finite-rank operators.
This paper establishes global well-posedness, scattering results, and polynomial stability for wave-type equations with singular potentials and data on by employing Yamazaki-type estimates on Lorentz spaces, fixed point arguments, and dispersive estimates within a weak- framework.
This paper constructs a non-trivial, renormalized Hamiltonian for supercritical spin-boson models, including the Weisskopf-Wigner spontaneous emission, by employing a non-unitary dressing transformation within the Hamiltonian formalism of constructive quantum field theory to resolve the issue of triviality found in unitarily-renormalized versions.
This paper introduces the class of weakly Demi Dunford-Pettis applications, investigates their relationships with weakly Dunford-Pettis and Demi Dunford-Pettis operators, and analyzes their behavior within Banach Lattices.
Motivated by recent finite-dimensional results, this paper establishes Jensen's inequality for partial traces within both semifinite and general non-tracial von Neumann algebras.
This paper investigates the number of isomorphism types of Banach spaces for compact spaces of a given weight, proving that there are exactly $2^\kappa\kappa\omega_12^{\omega_1}$) depends on additional set-theoretic axioms such as the Continuum Hypothesis or Baumgartner's axiom.
This paper characterizes the nuclearity of Toeplitz operators between Fock spaces and with Borel measure symbols, establishing necessary and sufficient conditions via the Berezin transform for the case while demonstrating that separate conditions are required when .