Applications of semigroups of operators to non-elliptic differential operators

Zheng, Qian

doi:10.1007/bf02886170

Cited by 9 publications

(13 citation statements)

References 35 publications

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“…We know that the operator P(A) is closable and that the following holds (cf. [46], [25], [20] and [18] for further information): Assuming that E is a function space on which translations are uniformly bounded and strongly continuous, the obvious choice for A j is −i∂/∂x j (notice also that E can be consisted of functions defined on some bounded domain [5], [25], [46], [47]). If P(x) = |η|≤N a η x η , x ∈ R n and E is such a space (for example, L p (R n ) with p ∈ [1, ∞), C 0 (R n ) or BUC(R n )), then it is not difficult to prove that P(A) is nothing else but the operator Let p ∈ [1, ∞].…”

Section: Degenerate Time-fractional Equations Associated With Abstracmentioning

confidence: 99%

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Degenerate abstract Volterra equations in locally convex spaces

Kostić

2017

Filomat

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In the paper under review, we analyze various types of degenerate abstract Volterra integrodifferential equations in sequentially complete locally convex spaces. From the theory of non-degenerate equations, it is well known that the class of (a, k)-regularized C-resolvent families provides an efficient tool for dealing with abstract Volterra integro-differential equations of scalar type. Following the approach of T.-J. Xiao and J. Liang [41]-[43], we introduce the class of degenerate exponentially equicontinuous (a, k)regularized C-resolvent families and discuss its basic structural properties. In the final section of paper, we will look at generation of degenerate fractional resolvent operator families associated with abstract differential operators.

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Section: Degenerate Time-fractional Equations Associated With Abstracmentioning

confidence: 99%

“…Acknowledgements. The author would like to thank Professors M. Li and Q. Zheng for sending him the book [47].…”

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confidence: 99%

Degenerate abstract Volterra equations in locally convex spaces

Kostić

2017

Filomat

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“…. , A ′ n ); we refer the reader to [57] and [22, Section 4] for the definition of a closable operator P (A ′ ), where P (x) is a complex polynomial in n variables, and for more details about functional calculus for commuting generators of bounded…”

Section: Theorem 23 Assume That the Function K(t) Satisfiesmentioning

confidence: 99%

Degenerate multi-term fractional differential equations in locally convex spaces

Kostić

2016

Publ Inst Math (Belgr)

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“…One of the limitations is that the resolvent sets of generators must contain a right half-plane; however, it is known that there are many nonelliptic operators whose resolvent sets are empty see, e.g., 4 . On the other hand, the resolvent sets of the generators of regularized semigroups need not be nonempty; this makes it possible to apply the theory of regularized semigroups to nonelliptic operators, such as coercive operators and hypoelliptic operators see [5][6][7][8] . Moreover, for second-order equations, Zheng 9 considered coercive differential operators with constant coefficients generating integrated cosine functions.…”

Section: Introductionmentioning

confidence: 99%