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Quasiaffine transforms of Hilbert space operators
Ampliation quasisimilarity was applied as a tool in Foias and Pearcy (J Funct Anal 219:134–142, 2005) to reduce the hyperinvariant subspace problem...
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On power bounded operators with holomorphic eigenvectors. II
In [U] (among other results), M. Uchiyama gave necessary and sufficient conditions for contractions to be similar to the unilateral shift S of...
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Artificial neural networks with uniform norm-based loss functions
We explore the potential for using a nonsmooth loss function based on the max-norm in the training of an artificial neural network without hidden...
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WHEN IS THE AUTOMORPHISM GROUP OF AN AFFINE VARIETY NESTED?
For an affine algebraic variety X , we study the subgroup Aut alg ( X ) of the group of regular automorphisms Aut( X ) of X generated by all the connected...
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Pluquasisimilar Hilbert space operators
In [BJKP] the concept of pluquasisimilarity was introduced, which is a relation between two operators, implemented by systems of intertwining...
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Introductory Results
This chapter summarizes the essential background required for the rest of the book. Its purpose is notation, terminology, and basics. As for basics,...
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Orbit Closures of the Witt Group Actions
We prove that for any prime p there exists an algebraic action of the two-dimensional Witt group W 2 ( p ) on an algebraic variety X such that the...
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FACTORIAL AFFINE Gα-VARIETIES ISOMORPHIC TO HYPERSURFACES OF DANIELEWSKI TYPE
Let k be an algebraically closed field of characteristic zero and B a factorial affine k -domain equipped with a locally nilpotent derivation δ . We...
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On power bounded operators with holomorphic eigenvectors
In [17], M. Uchiyama gave necessary and sufficient conditions for contractions to be quasiaffine transforms, quasisimilar, or similar to unilateral...
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Pell surfaces
In 1826 Abel started the study of the polynomial Pell equation x 2 − g ( u ) y 2 = 1. Its solvability in polynomials x ( u ), y ( u ) depends on a certain...
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The local fundamental group of a Kawamata log terminal singularity is finite
We prove a conjecture of Kollár stating that the local fundamental group of a klt singularity x is finite. In fact, we prove a stronger statement,...
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A G2-period of a Fourier coefficient of an Eisenstein series on E6
We calculate a G 2 -period of a Fourier coefficient of a cuspidal Eisenstein series on the split simply-connected group E 6 , and relate this period to...
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Quasiprojective varieties over algebraically closed fields
In this chapter we give a quick introduction to algebraic varieties, focusing mainly on the properties used in parts 2 and 3. Appendix...
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Examples of cyclic polynomially bounded operators that are not similar to contractions
The question if a polynomially bounded operator is similar to a contraction was posed by Halmos and was answered in the negative by Pisier. His...
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G-Closures of a Set of Isotropic Dielectrics with Respect to One-Dimensional Wave Propagation
This chapter is about G-closures (i.e., the sets of invariant properties) of the regular mixtures of two isotropic dielectrics distributed in 1D +...