### Abstract

Let (Formula presented.) be the symmetric tube domain associated with the Jordan algebra (Formula presented.), (Formula presented.), (Formula presented.), or (Formula presented.), and (Formula presented.) be its Shilov boundary. Also, let (Formula presented.) be a degenerate principal series representation of (Formula presented.). Then we investigate the Bessel integrals assigned to functions in general (Formula presented.)-types of (Formula presented.). We give individual upper bounds of their supports, when (Formula presented.) is reducible. We also use the upper bounds to give a partition for the set of all (Formula presented.)-types in (Formula presented.), that turns out to explain the (Formula presented.)-module structure of (Formula presented.). Thus, our results concretely realize a relationship observed by Kashiwara and Vergne [(Formula presented.)-types and singular spectrum, in Noncommutative Harmonic analysis, Lecture Notes in Mathematics, Vol. 728 (Springer, 1979), pp. 177–200] between the Fourier supports and the asymptotic (Formula presented.)-supports assigned to (Formula presented.)-submodules in (Formula presented.).

Original language | English |
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Journal | International Journal of Mathematics |

DOIs | |

Publication status | Accepted/In press - 2018 Apr 10 |

### Fingerprint

### Keywords

- confluent hypergeometric functions
- degenerate principal series representations
- Euclidean Jordan algebras
- symmetric tube domains

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*International Journal of Mathematics*. https://doi.org/10.1142/S0129167X18500258

**Fourier supports of K-finite Bessel integrals on classical tube domains.** / Kobana, Tetsuya; Kodaira, Kaoru; Miyazaki, Takuya.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Fourier supports of K-finite Bessel integrals on classical tube domains

AU - Kobana, Tetsuya

AU - Kodaira, Kaoru

AU - Miyazaki, Takuya

PY - 2018/4/10

Y1 - 2018/4/10

N2 - Let (Formula presented.) be the symmetric tube domain associated with the Jordan algebra (Formula presented.), (Formula presented.), (Formula presented.), or (Formula presented.), and (Formula presented.) be its Shilov boundary. Also, let (Formula presented.) be a degenerate principal series representation of (Formula presented.). Then we investigate the Bessel integrals assigned to functions in general (Formula presented.)-types of (Formula presented.). We give individual upper bounds of their supports, when (Formula presented.) is reducible. We also use the upper bounds to give a partition for the set of all (Formula presented.)-types in (Formula presented.), that turns out to explain the (Formula presented.)-module structure of (Formula presented.). Thus, our results concretely realize a relationship observed by Kashiwara and Vergne [(Formula presented.)-types and singular spectrum, in Noncommutative Harmonic analysis, Lecture Notes in Mathematics, Vol. 728 (Springer, 1979), pp. 177–200] between the Fourier supports and the asymptotic (Formula presented.)-supports assigned to (Formula presented.)-submodules in (Formula presented.).

AB - Let (Formula presented.) be the symmetric tube domain associated with the Jordan algebra (Formula presented.), (Formula presented.), (Formula presented.), or (Formula presented.), and (Formula presented.) be its Shilov boundary. Also, let (Formula presented.) be a degenerate principal series representation of (Formula presented.). Then we investigate the Bessel integrals assigned to functions in general (Formula presented.)-types of (Formula presented.). We give individual upper bounds of their supports, when (Formula presented.) is reducible. We also use the upper bounds to give a partition for the set of all (Formula presented.)-types in (Formula presented.), that turns out to explain the (Formula presented.)-module structure of (Formula presented.). Thus, our results concretely realize a relationship observed by Kashiwara and Vergne [(Formula presented.)-types and singular spectrum, in Noncommutative Harmonic analysis, Lecture Notes in Mathematics, Vol. 728 (Springer, 1979), pp. 177–200] between the Fourier supports and the asymptotic (Formula presented.)-supports assigned to (Formula presented.)-submodules in (Formula presented.).

KW - confluent hypergeometric functions

KW - degenerate principal series representations

KW - Euclidean Jordan algebras

KW - symmetric tube domains

UR - http://www.scopus.com/inward/record.url?scp=85045117925&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85045117925&partnerID=8YFLogxK

U2 - 10.1142/S0129167X18500258

DO - 10.1142/S0129167X18500258

M3 - Article

JO - International Journal of Mathematics

JF - International Journal of Mathematics

SN - 0129-167X

ER -