C*-Algebras of Bergman Type Operators with Piecewise Constant Coefficients over Sectors

Espinoza-Loyola, Enrique; Karlovich, Yuri I.; Vilchis-Torres, O.

doi:10.1007/s00020-015-2226-5

Cited by 4 publications

(4 citation statements)

References 11 publications

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“…At the same time, p-step kernels can approximate continuous (or other class) kernels with arbitrary precision when p → ∞. All this shows that p-step kernels are noteworthy, see also [7].…”

Section: Introductionmentioning

confidence: 78%

“…Using (20) we obtain where D α (p ⋄ r, m) corresponds to the elementary matrix (δ(r, m)) r,m∈Pα in the algebra C |Pα|×|Pα| = C p |α| ×p |α| . Let A ∈ L be some operator of the form ( 6)- (7). Using (21), ( 22) we deduce that…”

Section: Proof Of Theorem 11mentioning

confidence: 99%

“…Remark. All the results can be easily extended to the case where A (6) acts on ⊕ M m=1 L 2 and the kernels A α (7) are M × M p-step matrices (this means that all entries of these matrices are p-step functions and, hence, the coefficients a α (7) are M × M constant matrices). The integral operators with p-step M × M matrix-valued kernels A α form an algebra L M .…”

Section: Introductionmentioning

confidence: 97%

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Mixed multidimensional integral operators with piecewise constant kernels and their representations

Kutsenko

2017

Linear and Multilinear Algebra

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We consider the algebra of mixed multidimensional integral operators. In particular, Fredholm integral operators of the first and second kind belongs to this algebra. For the piecewise constant kernels we provide an explicit representation of the algebra as a product of simple matrix algebras. This representation allows us to compute the inverse operators (or to solve the corresponding integral equations) and to find the spectrum explicitly. Moreover, explicit traces and determinants are also constructed. So, roughly speaking, the analysis of integral operators is reduced to the analysis of matrices. All the qualitative characteristics of the spectrum are preserved since only the kernels are approximated.

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Section: Introductionmentioning

confidence: 78%

Section: Proof Of Theorem 11mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

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Mixed multidimensional integral operators with piecewise constant kernels and their representations

Kutsenko

2017

Linear and Multilinear Algebra

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“…Such C * -algebras for bounded domains U with smooth boundaries were studied in [24] and [25]. The papers [12,13,15] (see also [20]) dealt with studying C * -algebras generated by the multiplication operators by piecewise continuous functions and by the Bergman and anti-Bergman projections B U,1 and BU,1 on the space L 2 (U) over domains U with piecewise Dini-smooth boundaries admitting Dini-smooth corners. These C * -algebras with a wider class of multiplication operators by piecewise slowly oscillating functions were studied in [14] by applying results of [43] on the C * -algebra Q = VMO ( ) ∩ L ∞ ( ) .…”

Section: Introductionmentioning

confidence: 99%

C*-Algebras of Poly-Bergman Type Operators With Piecewise Slowly Oscillating Coefficients

Espinoza-Loyola

Karlovich

2022

J Math Sci

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Given n, m ∈ ℕ and a simply connected uniform domain U ⊂ ℂ with a sufficiently smooth boundary U , we study the C * -algebra generated by the operators of multiplication by functions in ( ) , by the poly-Bergman projections B U,1 , … , B U,n and by the anti-poly-Bergman projections BU,1 , … , BU,m acting on the Lebesgue space L 2 (U) . The C * -algebra ( ) is generated by the set SO (U) of all bounded continuous functions on U that slowly oscillate at points of U and by the set PC( ) of all piecewise continuous functions on the closure U of U with discontinuities on a finite union of piecewise Dini-smooth curves that have one-sided tangents at every point z ∈ , possess a finite set Y = ∩ U , do not form cusps, and are not tangent to U at the points z ∈ Y . Making use of the Allan-Douglas local principle, the limit operators techniques, quasicontinuous maps, and properties of SO (U) functions, a Fredholm symbol calculus for the C * -algebra U,n,m ( ) is constructed and a Fredholm criterion for its operators is obtained. KeywordsPoly-Bergman and anti-poly-Bergman projections • Piecewise continuous function • Slowly oscillating function • C * -algebra • Fredholm symbol calculus • Fredholmness

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$${{\varvec{C}}}^*$$ C ∗ -Algebras of Poly-Bergman Type Operators Over Sectors

Karlovich

2017

Integr. Equ. Oper. Theory

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C*-Algebras of Bergman Type Operators with Piecewise Constant Coefficients over Sectors

Cited by 4 publications

References 11 publications

Mixed multidimensional integral operators with piecewise constant kernels and their representations

Mixed multidimensional integral operators with piecewise constant kernels and their representations

C*-Algebras of Poly-Bergman Type Operators With Piecewise Slowly Oscillating Coefficients

$${{\varvec{C}}}^*$$ C ∗ -Algebras of Poly-Bergman Type Operators Over Sectors

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